# Equivalent Equations

# Equivalent Equations

##### Problem 1

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

##### 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) $12x - 12 = 24$

##### Problem 3

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 $0.05n + 0.1d = 3.65$?

##### 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?

6) What is the standard deviation?

7) What is the median?

8) What is the IQR?

##### 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?

##### 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?