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.