Practice questions available in **McGraw Hill Math Grade 6 Answer Key PDF** **Lesson 17.5 Solving Equations and Inequalities by Substitution **will engage students and is a great way of informal assessment.

## McGraw-Hill Math Grade 6 Answer Key Lesson 17.5 Solving Equations and Inequalities by Substitution

**Exercises**

Question 1.

Sydney has a dozen eggs. He wants to bake a cake, but his mother says she needs 9 of the 12 eggs. What equation could he write to see how many eggs he will be able to use for his cake?

Answer:

Number of eggs he will be able to use for his cake = 3.

Explanation:

Number of eggs Sydney has = 12.

Number of eggs his mom needs = 9.

Number of eggs he will be able to use for his cake = Number of eggs Sydney has – Number of eggs his mom needs

= 12 – 9

= 3.

Question 2.

If Sydney’s cake recipe calls for 4 eggs, will he have enough eggs to bake the cake?

Answer:

No, he doesn’t have enough eggs to bake the cake because number of eggs he will be able to have are less than his cake recipe.

Explanation:

Number of eggs he will be able to use for his cake = 3.

Number of eggs Sydney’s cake recipe calls = 4.

Question 3.

If Sydney decides instead to make brownies that require only 3 eggs, will he have enough eggs to make the brownies?

Answer:

Yes, he can make brownies because he has enough eggs with him.

Explanation:

Number of eggs he will be able to use for his cake = 3.

Number of eggs he needs to make brownies = 3.

Question 4.

Kai has 4 red marbles, 3 blue marbles, 3 green marbles, and 2 yellow marbles. Kai wants to play a game with his brother that requires 6 marbles that are all the same color. Kai’s brother says he can bring 2 marbles of any color. Which color should Kai bring?

Answer:

Red Marbles color his brother should get because it total matches the number of marbles he needs to play with his brother.

Explanation:

Number of red marble Kai has = 4.

Number of blue marble Kai has = 3.

Number of green marble Kai has = 3.

Number of yellow marble Kai has = 2.

Number of marbles he needs to play with his brother = 6.

Number of marbles his brother said will bring of any color = 2.

Marbles color his brother should get:

Number of marbles his brother said will bring of any color + Number of red marble Kai has

= 2 + 4

= 6.

Number of marbles his brother said will bring of any color + Number of blue marble Kai has

= 2 + 3

= 5.

Number of marbles his brother said will bring of any color + Number of green marble Kai has

= 2 + 3

= 5.

Number of marbles his brother said will bring of any color + Number of yellow marble Kai has

= 2 + 2

= 4.

Question 5.

Write an equation that describes the total number of marbles in the game in question 4, using the letter m for the number of marbles Kai should bring.

Answer:

Total number of marbles Kai should bring = m = 2 + 4 = 6.

Explanation:

Number of red marble Kai has = 4.

Number of blue marble Kai has = 3.

Number of green marble Kai has = 3.

Number of yellow marble Kai has = 2.

Total number of marbles Kai should bring = m = 6.

Number of marbles his brother said will bring of any color + Number of red marble Kai has

= 2 + 4

= 6.

Question 6.

If \(\frac{4}{k}\) = 2, which of the following could k be the value of k?

(A) 1

(B) 2

(C) 3

(D) 4

Answer:

If \(\frac{4}{k}\) = 2, then k = 2.

(B) 2

Explanation:

If \(\frac{4}{k}\) = 2

=> 4 = 2 × k

=> 4 ÷ 2 = k

=> 2 = k.

Question 7.

The Ferris wheel costs 4 tickets for each rider. Sarah and Sadie want to ride together. Sarah has only 3 tickets left. Sadie will need to have at least how many tickets for them to ride together?

Answer:

Number of tickets Sadie will need to have for them to ride together = 5.

Explanation:

Cost of tickets the Ferris wheel costs for each rider = 4.

Number of tickets Sarah has left = 3.

Number of tickets needed for two riders = 2 × Cost of tickets the Ferris wheel costs for each rider

= 2 × 4

=8.

Number of tickets Sadie will need to have for them to ride together = Number of tickets needed for two riders – Number of tickets Sarah has left

= 8 – 3

= 5.

Question 8.

Write the total number of tickets Sarah and Sadie need in question 7 as an inequality, using x for the number of tickets Sadie will need.

Answer:

Number of tickets Sadie will need to have for them to ride together = 5.

Explanation:

Let the number of tickets Sadie will need to have for them to ride together be x.

Number of tickets needed for two riders = 8.

Number of tickets Sarah has left = 3.

Number of tickets needed for two riders – Number of tickets Sarah has left = x

= > 8 – 3 = x

=> 5 = x.