# Lesson 6

Equivalent Equations

• Let's investigate what makes two equations equivalent.

### Problem 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

Select all the equations that have the same solution as the equation $$3x-12=24$$.

A:

$15x-60=120$

B:

$3x=12$

C:

$3x=36$

D:

$x-4=8$

E:

$12x-12=24$

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 Select all the equations that have the same solution as $$2x - 5 = 15$$. A:$2x = 10$B:$2x = 20$C:$2(x - 5)= 15$D:$2x - 20 = 0$E:$4x - 10 = 30$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: 1. What is the mean? 2. What is the standard deviation? 3. What is the median? 4. What is the IQR? (From Algebra1, Unit 1, Lesson 14.) ### Problem 6 A basketball coach purchases bananas for the players on his team. The table shows total price in dollars, $$P$$, of $$n$$ bananas. Which equation could represent the total price in dollars for $$n$$ bananas? number of bananas total price in dollars 7 4.13 8 4.72 9 5.31 10 5.90 A:$P = 0.59n$B:$P = 5.90 - 0.59n$C:$P = \frac{5.90}{n}$D:$P = n + 0.59$(From Algebra1, Unit 2, Lesson 3.) ### Problem 7 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 numbers of dimes and 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.

A:

$(100, 0)$

B:

$(20, 50)$

C:

$(50, 20)$

D:

$(0, 100)$

E:

$(10, 36)$

(From Algebra1, Unit 2, Lesson 4.)

### Problem 8

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

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

A:

$(2,\text-3)$

B:

$(4,0)$

C:

$(5,\text-1)$

D:

$(0,\text-6)$

E:

$(2,3)$

(From Algebra1, Unit 2, Lesson 5.)

### Problem 9

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:

Point A

B:

Point B

C:

Point C

D:

Point D

(From Algebra1, Unit 2, Lesson 5.)