Refer to our Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Lesson 3.4 Answer Key Applications of Percent.
Texas Go Math Grade 7 Lesson 3.4 Answer Key Applications of Percent
Example 1
Marcus buys a varsity jacket from a clothing store in Arlington. The price of the jacket is $80 and the sales tax is 8%. What is the total cost of the jacket?
Step 1: Use a bar model to find the amount of the tax.
Draw a bar for the price of the jacket, $80. Divide it into 10 equal parts. Each part represents 10% of $80, or $8.
Then draw a bar that shows the sales tax: 8% of $80.
Because 8% is \(\frac{4}{5}\) of 10%, the tax is \(\frac{4}{5}\) of one part of the whole bar.
Each part of the whole bar is $8.
So, the sales tax is \(\frac{4}{5}\) of $8.
\(\frac{4}{5}\) × $8= $6.40
The sales tax is $6.40.
Step 2: To find the total cost of the jacket, add the price of the jacket and the sales tax.
Jacket price + Sales tax = Total cost
$80 + $6.40 = $86.40
Your Turn
Question 1.
Sharon wants to buy a shirt that costs $20. The sales tax is 5%. How much is the sales tax? What is her total cost for the shirt? __________
Answer:
Sales tax amount = Original cost × Sales tax percentage
= 20 × 5%
= 20 × 0.05
= $1
Total cost = Original cost + Sales tax amount
= 20 + 1
= $21
Example 2
Terry deposits $200 into a bank account that earns 3% simple interest per year. What Is the total amount in the account after 2 years?
Step 1 Find the amount of interest earned in one year. Then calculate the amount of interest for 2 years.
Write 3% as a decimal: 0.03
Interest Rate × Initial Deposit = Interest for 1 year
0.03 × $200 = $6
Interest for 1 year × 2 years = Interest for 2 years
$6 × 2 = $12
Step 2: Add the interest for 2 years to the initial deposit to find the total amount in his account after 2 years.
Initial deposit + Interest for 2 years = Total
$200 + $12 = $212
The total amount in the account after 2 years is $212.
Reflect
Question 2.
Write an expression you can use to find the total amount in Terry’s account.
Answer:
Combine the 3 expressions from Example 2 to form 1 expression.
Total = Initial deposit + Initial deposit × Interest rate × 2 years
Your Turn
Question 3.
Ariane borrows $400 on a 4-year loan. She is charged 5% simple interest per year. How much interest is she charged for 4 years? What is the total amount she has to pay back? ____________________
Answer:
Find the amount of interest earned in one year. Then calculate the amount of interest for 4 years.
Write 4% is a decimal: 0.04
Interest for 1 year = Interest rate × Initial loan
= 0.04 × $400
= $16
Interest, for 4 years = Interest for 1 year × 1 years
= $16 × 4
= $64
Add the interest for 4 years to the initial loan to find the total amount she has to pay back.
Total amount = Initial loan + Interest for 4 years
= $400 + $64
= $164
$64 of interest is charged in 4 years.
The total amount she has to back is $464.
Question 4.
Samuel orders four DVDs from an online music store. Each DVD costs $9.99. He has a 20% discount code, and sales tax is 6.75%. What is the total cost of his order?
Answer:
Start with calculating the cost of 4 CDs.
$9.99 × 4 = $39.96
Now, calculate the sales tax, then the cost of the CD’s with applied sales tax
Sales tax = Cost of 4 CD’s * Sales tax percentage
= $39.96 × 6.75%
= $39.96 × 0.0675
≈ $2.7
Cost with applied sales tax = Original cost + Sales tax
= $39.96 + $2.7
= $42.26
Having the cost with applied sales tax, we have to apply the 20% discount
Amount of discount = $42.26 × 20%
= $42.26 × 0.2
≈ $8.45
Total cost = $42.26 – $8.45
= $33.81
Texas Go Math Grade 7 Lesson 3.4 Guided Practice Answer Key
Question 1.
5% of $30 = ____________.
Answer:
Write percentage as decimals, then calculate the task.
5% = 0.05
$30 × 0.05 = $1.5
Question 2.
15% of $70 = _____________
Answer:
Write percentage as decimals, then calculate the task.
15% = 0.15
$70 × 0.15 = $10.5
Question 3.
0.4% of $100 = ______________________
Answer:
Write percentage as decimals, then caLculate the task.
0.4% = 0.004
$100 × 0.004 = $0.4
Question 4.
150% of $22 = ________________
Answer:
Write percentage as decimaLs, then calculate the task.
150% = 1.5
$22 × 1.5 = $33
Question 5.
1% of $80 ___________________
Answer:
Write percentage as decimals, then calculate the task.
1% = 0.01
$80 × 0.01 = $0.8
Question 6.
200% of $5 = _______________
Answer:
Write percentage as decimals, then caLculate the task.
200% = 2
$5 × 2 = $10
Question 7.
Brandon buys a radio for $43.99 in a state where the sales tax is 7%. (Example 1)
a. How much does he pay in taxes? _______________________________
Answer:
Sales tax amount = Original cost × Sales tax percentage
= $43.99 × 7%
= $43.99 × 0.07
b. What is the total Brandon pays for the radio? ______________________
Answer:
Total cost = Original cost + Sales tax amount
= $43.99 + $3.08
= $47.07
Question 8.
Luisa’s restaurant bill comes to $75.50, and she leaves a 15% tip. What is Luisa’s total restaurant bill? (Example 1)
Answer:
Tip amount = Bill × Tip percentage
= $73.50 × 15%
= $75.50 × 0.15
≈ 811.33
Total cost = Bill + Tip amount
= $75.50 + $11.33
= $86.83
Luisa’s total restaurant bill is $86.63.
Question 9.
Joe borrowed $2,000 from the bank at a rate of 7% simple interest per year. How much interest did he pay in 5 years? (Example 2)
Answer:
Find the amount of interest earned in one year. Then calculate the amount of interest for 5 years.
Write 7% as a decimal: 0.07
Interest for 1 year = Interest rate × InitiaI loan
= 0.07 × $2000
= $140
Interest for 5 years = Interest for 1 year × 5 years
= $140 × 5
= $700
He paid $700 of interest in 5 years.
Question 10.
You have $550 in a savings account that earns 3% simple interest each year. How much will be ¡n your account in 10 years? (Example 2)
Answer:
Find the amount of interest earned in one year. Then calculate the amount of interest for 10 years.
Write 3% as a decimal: 0.03
Interest for 1 year = Interest rate × Initial amount.
= 0.03 × $550
= $16.5
Interest for 10 years – Interest for 1 year × 10 years
= $16.5 × 10
= $165
Add the interest, for 10 years to the initial amount to find the total amount on the account.
Total amount = Initial amount + Interest for 10 years
= $550 + $165
= $715
The balance on account will be $715.
Question 11.
Martin finds a shirt on sale for 10% off at a department store. The original price was $20. Martin must also pay 8.5% sales tax. (Example 3)
a. How much is the shirt before taxes are applied? ________________
Answer:
Apply the 10% sale on the original cost..
Discount amount = Original cost × Sale percentage
= $20 × 10%
= $20 × 0.1
= $2
Sale price = Original cost – Discount amount
= $20 – $2
= $18
The shirt before taxes are applied cost $18.
b. How much is the shirt after taxes are applied? ____________________
Answer:
Apply the sales tax to the cost obtained in a. subtask.
Sales tax amount = Sale price × Sales tax
= $18 × 8.5%
= $18 × 0.085
= $1.53
Total cost = Sale price + Sales tax amount
= $18 + $1.53
= $19.53
The shirt after taxes are applied cost $19.53.
Question 12.
Teresa’s restaurant bill comes to $29.99 before tax. If the sales tax is 6.25% and she tips the waiter 20%, what is the total cost of the meal? (Example 3)
Answer:
Calculate the sales tax separately, then calculate the tip. and then add the sales tax and the tip to the bill for the meal to find the total.
Sales tax: 0.0625 × $29.99 ≈ $1.87
Tip: 0.2 × 829.99 86
Total cost = Meal + Tip + Sales tax
= $29.99 + $6 + $1.87
= $37.86
Estimate the sales tax and tip. Sales tax is about 10% plus 20% for tip gives %30. Find 30 of the bill: 0.3 × $29.99 ≈ $9. Add this to the bill: $29.99 + $9 = $38.99. The total cost should be about $39.
Essential Question Check-In
Question 13.
How can you determine the total cost of an item including tax if you know the price of the item and the tax rate?
Answer:
First, calculate the Sales tax amount by multiplying Original cost by Sales tax.
Then calculate the Total cost by adding Original cost and Sales tax amount.
Texas Go Math Grade 7 Lesson 3.4 Independent Practice Answer Key
Question 14.
Emily’s meal costs $32.75 and Darren’s meal costs $39.88. Emily treats Darren by paying for both meals, and leaves a 14% tip. Find the total cost.
Answer:
The tip rate is 11%.
The total cost will be sum of the meal and the tip.
Meal: $32.75 + $39.88 = $72.63
Tip: $72.63 × 0.14 = $10.17
Total cost: $72.63 + $10.17 = $82.8
The total cost is $82.8.
Question 15.
The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.65, and they leave a 20% tip. If the tip applies to the cost of the meal before the discount, what is the total cost of the meal?
Answer:
The total cost will be sum of the tip before discount and the meal with the discount.
The tip rate is 20%.
The discount is 15%.
Tip: $78.65 × 0.2 = $15.73
Discount : $78.65 × 0. 15 = $11 .80
Meal with discount: $78.05 – $11.80 = $66.85
Total cost: $66.85 + $15.73 = $82.58
The total cost of the meal is $82.58.
Question 16.
A jeweler buys a ring from a jewelry maker for $125. He marks up the price by 135% for sale in his store. What is the selling price of the ring with 7.5% sales tax?
Answer:
The markup rate is 135%.
The sales tax is 7.5%.
The selling price will be sum of calculating sales tax and the markup price separately.
Sales lax: $125 × 0.075 = $9.38
Markup price: $125 × 1.35 = $168.75
Selling Price: $168.75 + $9.38 = $178.13
The selling price of the ring is $178.13.
Question 17.
Luis wants to buy a skateboard that usually sells for $79.99. All merchandise is discounted by 12%. What is the total cost of the skateboard if Luis has to pay a state sales tax of 6.75%?
Answer:
The discount is 12%.
The sales tax is 6.75%.
Tue total cost will be sum of discounted price and sales tax on discounted price.
Discount : $79.99 × 0.12 = $9.60
Discounted price: $79.99 – $9.60 = $70.39
Sales tax: $70.39 × 0.0675 = $4.75
Total cost: $70.39 + $4.75 = $75.14
Tue total cost of the skateboard is $75.14.
Question 18.
Kedar earns a monthly salary of $2,200 plus a 3.75% commission on the amount of his sales at a men’s clothing store. What would he earn this month if he sold $4,500 in clothing? Round to the nearest cent.
Answer:
The commission is 75%.
Kedar will earn the sum of his monthly salary and the commission of his sales.
Commission: $4,500 × 0.0375 = $168.75
Total salary: $2.200 + $168.75 = $2,368.75
Kedar would earn $2,368.75 this month.
Question 19.
Danielle earns a 7.25% commission on everything she sells at the electronics store where she works. She also earns a base salary of $750 per week. How much did she earn last week if she sold $4,500 in electronics merchandise? Round to the nearest cent.
Answer:
The commission is 7,25%.
Danielle will earn the sum of her weekly salary and the commission of her sales.
Commission: $4,500 × 0.0725 = $326.25
Total salary: $750 + $326.25 = $1,076.25
Danielle earned $1.076.25 last week.
Question 20.
Francois earns a weekly salary of $475 plus a 5.5% commission on sales at a gift chop. How much would he earn in a week if he sold $700 in goods? Round to the nearest cent.
Answer:
The commission is 5.5%.
Fraucois would earn the sum of his weekly salary and the commission of his sales.
Commission: $700 × 0.055 = $38.50
Total salary: $700 + $38.50 = $738.50
Francois would earn $738.50 in a week.
Question 21.
Sandra is 4 feet tall. Pablo is 10% taller than Sandra, and Michaela ¡s 8% taller than Pablo. a. Explain how to find Michaela’s height with the given information.
Answer:
First find Pablo’s height by applying 10% increase on Sandra’s height
Then, find Michaela’s height by applying 8% increase on Pablo’s height
Pablo: 4ft + 4 ft × 0.1 = 4.4 ft
Michaela: 4.4 ft + 4.4 ft × 0.08 = 4.752 ft
Michaela is 4752 ft tall.
b. What is Michaela’s approximate height in feet and inches?
Answer:
Convert the decimal part of her height to inches
1 ft = 12 in
0.752 ft = 0.752 × 12 in ≈ 9 in
Michaela is 4 ft 9 in tall.
Question 22.
Eugene wants to buy jeans at a store that is offering a $10 discount on every item. The tag on the jeans is marked 50% off. The original price is $49.98.
a. Find the final cost if the 50% discount is applied before the $10 discount.
Answer:
10$ discount: $49.98 – $10 = $39.98
Total cost: $39.98 = $39.98 × 0.5 = $19.99
The total cost is $19.99
b. Find the final cost if the $10 discount is applied before the 50% discount.
Answer:
50% discount: $49.98 – $49.98 × 0.5 = $24.99
Total cost: $24.99 – $10 = $14.99
The total cost is $14.99
Question 23.
Multistep Eric downloads the coupon shown and goes shopping at Gadgets Galore, where he buys a digital camera for $95 and an extra battery for $15.99.
a. What is the total cost if the coupon is applied to the digital camera?
Answer:
First, apply the discount on the digital camera. Total cost is the sum of the discounted camera and the extra battery.
Discounted camera: $95 – $95 × 0.1 = $95 – $9.50 = $85.50
Total cost: $85.50 + $15.99 = $101.49
The total cost is $101.49.
b. What is the total cost if the coupon is applied to the extra battery?
Answer:
First, apply the discount on the extra battery. Total cost is the sum of the camera and the discounted battery.
Discounted battery: $15.99 – $15.99 × 0.1 = $15.99 – $1.60 = $14.39
Total cost: $95 + $14.39 = $109.39
The total cost is $109.39.
c. To which item should Eric apply the discount? Explain.
Answer:
Eric should apply the discount on the camera as the total cost is lower that way.
d. Eric has to pay 8% sales tax after the coupon is applied. How much is his total bill if he applies the coupon to the digital camera?
Answer:
Apply the sales tax on the total cost from a. subtask.
Sales tax: $101.49 × 0.08 = $8.12
Total cost: $101.49 + $8.12 = $109.61
His total bill is $109.61.
Question 24.
Two stores are having sales on the same shirts. The sale at Store 1 is “2 shirts for $22” and the sale at Store 2 is “Each $12.99 shirt is 10% off”.
a. Explain how much will you save by buying at Store 1.
Answer:
First, apply the discount out the shirt and then multiply by 2.
$12.99 -$12.99 × 0.1 = $11.70
Total cost: $11.70 × 2 = $23.40
You will save $1.40 buying at Store 1.
b. If Store 3 has shirts originally priced at $20.98 on sale for 55% off, does it have a better deal than the other stores? Justify your answer.
Answer:
First, apply the discount on the shirt and then multiply by 2.
$20.9 – $20.9 × 0.55 = $2o.9 – $11.54 = $9.44
Total cost of 2 shirts: $9.44 × 2 = $18.88
The third store has the best deals of all stores, as the price of the T-shirt is the lowest.
H.O.T. Focus On Order Thinking
Question 25.
Analyze Relationships Marcus can choose between a monthly salary of $1,500 plus 5.5% of sales or $2,400 plus 3% of sales. He expects sales between $5,000 and $10,000 a month. Which salary option should he choose? Explain.
Answer:
We will calculate both salaries by first calculating sales commission and then adding to the base of the monthly salary.
Sales are expected to be between 5000 and 1000. We calculate both ends of the expected sales.
First salary option:
Base = $1500
Sales percentage = 5.5%
$5000 × 0.055 = $275
$10000 × 0.055 = $550
$1500 + $275 ≤ Salary ≤ $1500 + $550
$1775 ≤ Salary ≤ $2050
Second salary option:
Base = $2400
Sales percentage = 3%
$5000 × 0.03 = $150
$10000 × 0.03 = $300
$2400 + $150 ≤ Salary ≤ $2400 + $300
$2550 ≤ Salary ≤ $2700
It is obvious 110W that the second salary option would be greater than the first. Thus, Marcus should choose the second salary option.
Question 26.
Multistep In chemistry class, Bob recorded the volume of a liquid as 13.2 mL. The actual volume was 13.7 mL. Use the formula to find percent error of Bob’s measurement to the nearest tenth of a percent.
Percent Error = \(\frac{\mid \text { Experimental Value }-\text { Actual Value| }}{\text { Actual Value }}\) × 100%
Answer:
Insert given values into the formula
Experimental value = 13.2 mL
