Equivalent Equations

ID: mituf-gupug
Created by Illustrative MathIllustrative Math
Subject: Algebra, Algebra 2
Grade: 8-9

Equivalent Equations

Classroom:
Due:
Student Name:
Date Submitted:
Problem 1

1) Which equation is equivalent to the equation 6x+9=126x + 9 = 12?

a) x+9=6 x + 9 = 6 b) 2x+3=4 2x + 3 = 4 c) 3x+9=6 3x + 9 = 6 d) 6x+12=9 6x + 12 = 9
Problem 2

2) Select all the equations that have the same solution as the equation 3x12=243x - 12 = 24. Write each corresponding letter in the answer box and separate letters with commas.

a) 15x60=12015x - 60 = 120 \quad\quad b) 3x=123x = 12 \quad\quad c) 3x=363x = 36 \quad\quad d) x4=8x - 4 =8 \quad\quad e) 12x12=2412x - 12 = 24

Problem 3

3) Jada has a coin jar containing nn nickels and dd dimes worth a total of $3.65. The equation 0.05n+0.1d=3.650.05n + 0.1d = 3.65 is one way to represent this situation.

Which equation is equivalent to the equation 0.05n+0.1d=3.650.05n + 0.1d = 3.65?

a) 5n+d=365 5n + d = 365 b) 0.5n+d=365 0.5n + d = 365 c) 5n+10d=365 5n + 10d = 365 d) 0.05d+0.1n=365 0.05d + 0.1n = 365
Problem 4

4) Select all the equations that have the same solution as 2x5=152x - 5 = 15. Write each corresponding letter in the answer box and separate letters with commas.

a) 2x=102x = 10 \quad \quad b) 2x=202x = 20 \quad \quad c) 2(x5)=152(x - 5) = 15 \quad \quad d) 2x20=02x - 20 = 0 \quad \quad e) 4x10=304x - 10 = 30 \quad \quad f) 15=52x15 = 5 - 2x

Problem 5

The number of hours spent in an airplane on a single flight is recorded on a dot plot. The mean is 5 hours and the standard deviation is approximately 5.82 hours. The median is 4 hours and the IQR is 3 hours. The value 26 hours is an outlier that should not have been included in the data.

A template for answering this question. Ask your instructor for an alternative.

When the outlier is removed from the data set:

5) What is the mean?

Show Work

6) What is the standard deviation?

Show Work

7) What is the median?

Show Work

8) What is the IQR?

Show Work
Problem 6

9) A basketball coach purchases bananas for the players on his team. The table shows total price in dollars, PP, of nn bananas.

number of bananastotal price in dollars74.1384.7295.31105.90\begin{array}{|c|c|} \hline \\[-1em] \textbf{number of bananas} & \textbf{total price in dollars} \\[-1em] \\ \hline \\[-1em] 7 & 4.13 \\[-1em] \\ \hline \\[-1em] 8 & 4.72 \\[-1em] \\ \hline \\[-1em] 9 & 5.31 \\[-1em] \\ \hline \\[-1em] 10 & 5.90 \\[-1em] \\ \hline \end{array}

Which equation could represent the total price in dollars for nn bananas?

a) P=0.59n P = 0.59n b) P=5.900.59n P = 5.90 - 0.59n c) P=5.90n P = \frac{5.90}{n} d) P=n+0.59 P = n + 0.59
Problem 7

10) Kiran is collecting dimes and quarters in a jar. He has collected $10.00 so far and has dd dimes and qq quarters. The relationship between the number of dimes and the number of quarters, and the amount of money in dollars is represented by the equation 0.1d+0.25q=100.1d + 0.25q = 10.

Select all the values (d,q)(d,q) that could be solutions to the equation. Write each corresponding letter in the answer box and separate letters with commas.

a) (100,0)(100, 0) \quad \quad b) (20,50)(20, 50) \quad \quad c) (50,20)(50, 20) \quad \quad d) (0,100)(0, 100) \quad \quad e) (10,36)(10, 36)

Problem 8

Here is a graph of the equation 3x2y=123x - 2y = 12.

A template for answering this question. Ask your instructor for an alternative.

11) Select all coordinate pairs that represent a solution to the equation.

a) (2,3)(2, -3) \quad \quad b) (4,0)(4, 0) \quad \quad c) (5,1)(5, -1) \quad \quad d) (0,6)(0, -6) \quad \quad e) (2,3)(2, 3)

Problem 9

12) Jada bought some sugar and strawberries to make strawberry jam. Sugar costs $1.80 per pound, and strawberries cost $2.50 per pound. Jada spent a total of $19.40.

Which point on the coordinate plane could represent the pounds of sugar and strawberries that Jada used to make jam?

A template for answering this question. Ask your instructor for an alternative.
a) Point A\text{Point A}b) Point B\text{Point B}c) Point C\text{Point C}d) Point D\text{Point D}