All the solutions provided in **McGraw Hill Math Grade 5 Answer Key PDF Chapter 9 Lesson 11 Problem Solving: Working Backwards **are as per the latest syllabus guidelines.

## McGraw-Hill Math Grade 5 Answer Key Chapter 9 Lesson 11 Problem Solving: Working Backwards

**Solve**

Question 1.

Regina and Alicia had 4\(\frac{1}{2}\) cups of water at the end of a day of driving. They drank 8\(\frac{1}{4}\) cups before lunch and 11\(\frac{1}{4}\) cups in the afternoon. How much water did they start with?

Answer:

Number of cups of water they start with = 24.

Explanation:

Number of cups of water Regina and Alicia had at the end of a day of driving = 4\(\frac{1}{2}\).

Number of cups of water they drank before lunch = 8\(\frac{1}{4}\).

Number of cups of water they drank in the afternoon = 11\(\frac{1}{4}\).

Number of cups of water they start with = Number of cups of water Regina and Alicia had at the end of a day of driving + Number of cups of water they drank before lunch + Number of cups of water they drank in the afternoon

= 4\(\frac{1}{2}\) + 8\(\frac{1}{4}\) + 11\(\frac{1}{4}\)

= [(8 + 1) ÷ 2] + [(32 + 1) ÷ 4] + [(44 + 1) ÷ 4]

= \(\frac{9}{2}\) + \(\frac{33}{4}\) + \(\frac{45}{4}\)

= [(9 × 2) ÷ (2 × 2)] + \(\frac{33}{4}\) + \(\frac{45}{4}\)

= \(\frac{18}{4}\) + \(\frac{33}{4}\) + \(\frac{45}{4}\)

= (18 + 33 + 45) ÷ 4

= 96 ÷ 4

= 24.

Question 2.

A small shop has 5.9 pounds of lunch meat at the end of Friday. The shop sold 4.9 pounds on Friday morning and 9.35 pounds on Friday afternoon. How many pounds of lunchmeat did the store start with?

Answer:

Number of pounds of lunchmeat the store start with = 20.15.

Explanation:

Number of pounds of lunch meat a small shop has at the end of Friday = 5.9.

Number of pounds of lunch meat a small shop on Friday morning = 4.9.

Number of pounds of lunch meat a small shop on Friday afternoon = 9.35.

Number of pounds of lunchmeat the store start with = Number of pounds of lunch meat a small shop has at the end of Friday + Number of pounds of lunch meat a small shop on Friday morning + Number of pounds of lunch meat a small shop on Friday afternoon

= 5.9 + 4.9 + 9.35

= 10.8 + 9.35

= 20.15.

Question 3.

Use the digits 7, 3, 6, 5, 1, and 9 to write three numbers less than 600,000 but greater than 500,000. Use each digit only once for each number.

Answer:

Three numbers less than 600,000 but greater than 500,000.

=> 513679.

=> 531679.

=> 561379.

Question 4.

Ms. Torres is on a road trip. She drives a total of 2,731.82 miles in three weeks. She drives 791.38 miles the second week. She drives 1,086.14 miles the third week. How many miles did she drive the first week?

Answer:

Number of miles She drives in the first week = 854.3.

Explanation:

Number of miles She drives in three weeks = 2,731.82.

Number of miles She drives in the second week = 791.38.

Number of miles She drives in the third week = 1,086.14.

Number of miles She drives in the first week = Number of miles She drives in three weeks – (Number of miles She drives in the second week + Number of miles She drives in the third week)

= 2731.82 – (791.38 + 1086.14)

= 2731.82 -1877.52

= 854.3.

Question 5.

Mr. Kerry has 4 boxes of cocoa mix. Each box has 20 bags. He uses two cups of water and one bag of cocoa mix to make a mug of cocoa. How many cups of water will Mr Kerry use if he uses all the bags of cocoa mix?

Answer:

Number of cups of water if he uses all the bags of cocoa mix = 160.

Explanation:

Number of boxes of cocoa mix Mr. Kerry has = 4.

Number of bags each box has = 20.

Number of cups of water he uses to make a mug of cocoa = 2.

Number of bags he uses to make a mug of cocoa = 1.

Total number of bags of cocoa Mr. Kerry has = Number of boxes of cocoa mix Mr. Kerry has × Number of bags each box has

= 4 × 20

= 80.

Number of cups of water if he uses all the bags of cocoa mix = Number of cups of water he uses to make a mug of cocoa × Total number of bags of cocoa Mr. Kerry has

= 2 × 80

= 160.

Question 6.

Ling is 56\(\frac{3}{4}\) in. tall. Lauren is 49\(\frac{1}{3}\) in. tall. How much taller is Ling than Lauren?

Answer:

7.42 inches taller is Ling than Lauren.

Explanation:

Number of inches height is Ling = 56\(\frac{3}{4}\)

Number of inches height is Lauren = 49\(\frac{1}{3}\)

Difference:

Number of inches height is Ling – Number of inches height is Lauren

= 56\(\frac{3}{4}\) – 49\(\frac{1}{3}\)

= [(224 + 3) ÷ 4] – [(147 + 1) ÷ 3]

= (227 ÷ 4) – (148 ÷ 3)

= 56.75 – 49.33

= 7.42 inches.