Solving Multi-Step Equations Answers

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Rona mixes 2 pounds of meat with some chopped vegetables to make a mixture. She divides the mixture into 4 equal portions. Each portion weighs 3 pounds. Which equation and solution shows the total amount of chopped vegetables she used in the mixture?

A
pounds of chopped vegetables
Option A
B
pounds of chopped vegetables
Option B
C
pound of chopped vegetables
Option C
D
pounds of chopped vegetables
Option D
2
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The Schwartz family spent a total of $111.75 for Internet service for 3 months. Eachmonth they received $5.50 as a credit on the bill. Which equation and solution showsthe cost of their monthly Internet service before the credit?

A
; the monthly Internet service is $31.75
Option A
B
; the monthly Internet service is $42.75
Option B
C
; the monthly Internet service is $42.75
Option C
D
; the monthly Internet service is $31.75
Option D
3

Zachary is solving the following equation.Which is the best first step to begin to simplify the equation?

Question illustration
A
Multiply both sides of the equation by .
Option A
B
Divide both sides of the equation by .
Option B
C
Distribute over (x – 8).
Option C
D
Distribute over (x – 8).
Option D
4

Mr. Reddick has 74 total yards of red and blue felt to distribute to students in his art class. Each of his 20 students gets 2.5 yards of blue felt for the project. He also gives each student an equal amount of red felt. How much red felt does each student get?

A
1.2 yd
B
3.7 yd
C
12 yd
D
24 yd
5

Celia uses the steps below to solve the equation .Step 1Distribute over the expression in parentheses.Step 2Simplify like terms.Step 3Subtract 3 from both sides of the equation.Step 4Divide both sides of the equation by –14.Which corrects the error in the step in which Celia made the first error?

Question illustration
A
In step 1, she should have also distributed over 2d, to get .
Option A
B
In step 1, she should have also distributed over –16d, to get .
Option B
C
In step 3, she should have added 3 to both sides of the equation to get .
Option C
D
In step 3, she should have first divided both sides by –14 to get .
Option D
6

A group of 4 friends went to lunch and spent a total of $40, which included the $34 food bill and the tip. They decided to split the bill and tip evenly among themselves.One of the friends used the equation to represent the situation, where t represents the total amount of the tip. Which describes the amount each friend paid for the food and for the tip?

Question illustration
A
Each friend paid $8.50 for the food and $1.50 for the tip.
B
Each friend paid $10.00 for the food and $6.00 for the tip.
C
Each friend paid $8.50 for the food and $6.00 for the tip.
D
Each friend paid $10.00 for the food and $1.50 for the tip.
7

Rita makes and sells necklaces. The materials to make each necklace cost $2.75. Last week she made 8 necklaces and wants to make a total profit of $78. Using the equation , Rita determined that she needs to sell each necklace for $7 to make a total profit of $78. Which error did Rita make?

Question illustration
A
Although she has the correct equation, she needs to sell each necklace for $12.50.
B
Although she has the correct solution, she should have used the equation .
Option B
C
The equation should be , and she needs to sell each necklace for $12.50.
Option C
D
The equation should be , and she needs to sell each necklace for $75.25.
Option D
8

What is the value of r in the equation?

Question illustration
A
–6
B
–4
C
4
D
6
9

Nico, Aditi, Erick, Raj, and Sandra are solving the equation.Each student begins to solve the problem as shown.NicoAditiErickRajSandraWhich students are correct in their approach to solving the problem? Select three options.

Question illustration
A
Nico
B
Aditi
C
Erick
D
Raj
E
Sandra
10

A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves. Which equations and solutions describe the situation? Select two options.

A
The equation represents the situation, where x is the food bill.
Option A
B
The equation represents the situation, where x is the food bill.
Option B
C
The solution represents the total food bill.
Option C
D
The solution represents each friend’s share of the food bill and tip.
Option D
E
The equation represents the situation, where x is the food bill.
Option E

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