# Equivalent Equations

ID: mituf-gupug
Illustrative Math
Subject: Algebra, Algebra 2

# Equivalent Equations

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##### Problem 1

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

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

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

a) ﻿$15x - 60 = 120 \quad\quad$﻿ b) ﻿$3x = 12 \quad\quad$﻿ c) ﻿$3x = 36 \quad\quad$﻿ d) ﻿$x - 4 =8 \quad\quad$﻿ e) ﻿$12x - 12 = 24$﻿

3) Jada has a coin jar containing ﻿$n$﻿ nickels and ﻿$d$﻿ dimes worth a total of $3.65. The equation ﻿$0.05n + 0.1d = 3.65$﻿ is one way to represent this situation. Which equation is equivalent to the equation ﻿$0.05n + 0.1d = 3.65$﻿? a) $5n + d = 365$b) $0.5n + d = 365$c) $5n + 10d = 365$d) $0.05d + 0.1n = 365$ ##### Problem 4 4) Select all the equations that have the same solution as ﻿$2x - 5 = 15$﻿. Write each corresponding letter in the answer box and separate letters with commas. a) ﻿$2x = 10 \quad \quad$﻿ b) ﻿$2x = 20 \quad \quad$﻿ c) ﻿$2(x - 5) = 15 \quad \quad$﻿ d) ﻿$2x - 20 = 0 \quad \quad$﻿ e) ﻿$4x - 10 = 30 \quad \quad$﻿ f) ﻿$15 = 5 - 2x$﻿ ##### 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. 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, ﻿$P$﻿, of ﻿$n$﻿ bananas. ﻿$\begin{array}{|c|c|} \hline \\[-1em] \textbf{number of bananas} & \textbf{total price in dollars} \\[-1em] \\ \hline \\[-1em] 7 & 4.13 \\[-1em] \\ \hline \\[-1em] 8 & 4.72 \\[-1em] \\ \hline \\[-1em] 9 & 5.31 \\[-1em] \\ \hline \\[-1em] 10 & 5.90 \\[-1em] \\ \hline \end{array}$﻿ Which equation could represent the total price in dollars for ﻿$n$﻿ bananas? a) $P = 0.59n$b) $P = 5.90 - 0.59n$c) $P = \frac{5.90}{n}$d) $P = n + 0.59$ ##### Problem 7 10) Kiran is collecting dimes and quarters in a jar. He has collected$10.00 so far and has ﻿$d$﻿ dimes and ﻿$q$﻿ 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 ﻿$0.1d + 0.25q = 10$﻿.

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

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

##### Problem 8

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

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

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

##### 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) $\text{Point A}$b) $\text{Point B}$c) $\text{Point C}$d) $\text{Point D}$