# 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 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 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 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 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 Unit 2, Lesson 5.)