Question

Question 1:
Which of the following expressions are equivalent to −3.5(2 − 3n) − 2.5n?

A. −7 − 8n
B. −7 + 8n
C. −7 − 13n
D. −7 − n(10.5 − 2.5)
E. −7 + n(10.5 − 2.5)

Question 2:
During his workouts last week, Allen jogged the same amount of time each day for 6 days. Use the following information to determine the number of minutes Allen jogged each day:

During each workout, he jogged and he rode his bike.
He rode his bike for 45 minutes each day.
He worked out for a total of 360 minutes last week.
What is the number of minutes that Allen jogged each day last week? Enter your answer in the box below.

Question 3:
Marla bought one necklace and two bracelets for $67.50. Use the following information to determine the amount she paid for each bracelet:

The price of the necklace was $27.
The bracelets were both the same price.
Enter your numerical answer only in the box; do not include the dollar sign.


Question 4:
Two equations are shown:

Equation 1: 3/4(x−12)=12
Equation 2: 3/4y−12=12
Solve each equation. Then, enter a number in each box to make this statement true.

The value of x is:


The value of y is:

Answer 1

Q1: D
Q2: 45 minutes
Q3: 40.50
Q4: x=28, y=32

Answer 2

Answer:

1.) B. -7+8n; 2.) 15; 3.) 20.25; 4.) x=28 and y=32.

Step-by-step explanation:

1.) Simplifying our expression,

-3.5(2-3n)-2.5n

Use the distributive property:

-3.5(2)-3.5(-3n)-2.5n

-7+10.5n-2.5n

Combine like terms:

-7+8n

2.) Allen worked out for 360 minutes over 6 days.  This is 360/6 = 60 minutes per day.

He rode his bike for 45 minutes each day; this leaves

60-45 = 15 minutes for jogging each day.

3.) Marla spent a total of $67.50.  $27 of this was for the necklace; that leaves

67.50-27 = 40.50 for the two bracelets.  This means each one is

40.50/2 = 20.25.

4.) For equation 1:

3/4(x-12)=12

Use the distributive property:

3/4(x)-3/4(12) = 12

3/4x-3/4(12/1) = 12

3/4x-(3*12)/(4*1) = 12

3/4x-36/4 = 12

3/4x-9 = 12

Add 9 to each side:

3/4x-9+9 = 12+9

3/4x = 21

Divide both sides by 3/4:

3/4x÷3/4 = 21÷3/4

x = 21/1÷3/4

To divide fractions, flip the second one and multiply:

x = 21/1×4/3

x = 84/3 = 28

For Equation 2:

3/4y-12 = 12

Add 12 to each side:

3/4y-12+12 = 12+12

3/4y = 24

Divide both sides by 3/4:

3/4y÷3/4 = 24/1÷3/4

y = 24/1×4/3

y = 96/3 = 32