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

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?
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?
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?
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?
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.
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
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?
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.