## Engage NY Eureka Math 8th Grade Module 4 Mid Module Assessment Answer Key

Question 1.
Write and solve each of the following linear equations.
a. Ofelia has a certain amount of money. If she spends $12, then she has $$\frac{1}{5}$$ of the original amount left. How much money did Ofelia have originally? Answer: Let x be the amount of money ofelia had x – 12 = $$\frac{1}{5}$$ x – $$\frac{1}{5}$$x – 12 + 12 = $$\frac{1}{5}$$ x – $$\frac{1}{5}$$ x +12 $$\frac{4}{5}$$ x = 12 x= 12 ∙ $$\frac{5}{4}$$ = $$\frac{60}{4}$$ Ofelia had$15.00 originally.

b. Three consecutive integers have a sum of 234. What are the three integers?
Let x be the first integer
x + x + 1 + x + 2 = 234
3x + 3 = 234
3x = 234 – 3
3x = 231
x = 77
The integers are 77, 78, and 79

c. Gil is reading a book that has 276 pages. He already read some of it last week. He plans to read 20 pages tomorrow. By then, he will be $$\frac{2}{3}$$of the way through the book. How many pages did Gil read last week?
Let x be the number of pages gil read last week.
x + 20 = $$\frac{2}{3}$$(276)
x + 20 = 184
x + 20 – 20 = 184 – 20
x = 164
Gil read 164 pages last week

Question 2.
a. Without solving, identify whether each of the following equations has a unique solution, no solution,
or infinitely many solutions.
i. 3x + 5 = – 2
Unique

ii. 6(x – 11) = 15 – 4x
Unique

iii. 12x + 9 = 8x + 1 + 4x
No solution

iv. 2(x – 3) = 10x – 6 – 8x
Infinitely many solutions

v. 5x + 6 = 5x – 4
No solution

b. Solve the following equation for a number x. Verify that your solution is correct.
– 15 = 8x + 1 -2 = x

-15 = 8(-2) + 1
-15 = -16 + 1
-15 = -15

c. Solve the following equation for a number x. Verify that your solution is correct.
7(2x + 5) = 4x – 9 – x
7(2x + 5) = 4x – 9 – x
14x + 35 = 4x – 9 – x
14x + 35 = 3x – 9
14x – 3x + 35 = 3x – 3x – 9
11x + 35 = -9
11x + 35 – 35 = -9 – 35
11x = -44
x = -4

7(2(-4) + 5) = 4(-4) – 9 – (-4)
7(-8 + 5) = -16 – 9 + 4
7(-3) = -25 + 4
-21 = -21

Question 3.
a. Parker paid $4.50 for three pounds of gummy candy. Assuming each pound of gummy candy costs the same amount, complete the table of values representing the cost of gummy candy in pounds. Answer: b. Graph the data on the coordinate plane. Answer: c. On the same day, Parker’s friend, Peggy, was charged$5 for 1 $$\frac{1}{2}$$ lb. of gummy candy. Explain in terms of the graph why this must be a mistake.
Even though 1$$\frac{1}{2}$$ pounds of candy isn’t a point on the graph, it is reasonable to believe it will fall in line with the other points. The cost of 1$$\frac{1}{2}$$ pounds of candy does not fit the pattern.