8th Grade Math - Unit 3 Linear Equations Review

The equation below represents a situation.

        10(x − 5) = 9x

Which word problem could the equation represent?

• A.

  Makayla has a number of U.S. and Canadian one-dollar bills. If 10 Canadian dollars is worth 9 U.S. dollars, and Makayla has 5 fewer Canadian dollar bills than U.S. dollar bills, how many U.S. dollar bills does she have?

• B.

  Each crate in Mr. Chin's storeroom has 10 diet sodas and 9 regular sodas. If the total number of regular sodas is 5 less than the total number of diet sodas, what is the total number of diet sodas in the storeroom?

• C.

  At Eat-All-You-Want, the barbecue sauce packet has 5 fewer calories than the sweet-n-sour packet. If 10 barbecue sauce packets have the same amount of calories as 9 sweet-n-sour packets, how many calories do the sweet-n-sour packets have?

• D.

  Andrew rides his bike at 10 miles per hour, and Boris rides at 9 miles per hour. If the boys ride in the same direction and Boris gets a 5-mile head start, after how many miles will Andrew catch up to him?

Tags

CCSS.7.EE.B.4A

The equation below represents a situation.

        x − 1.5 = 6 − x

Which word problem could the equation represent?

• A.

  Sasha bought 6 yards of material. She wants to cut it into 2 pieces so that the difference between the lengths of the pieces will be 1.5 yards. What would be the length, in yards, of one of the pieces?

• B.

  A container with 6 liters of water starts leaking into a bucket that already has 1.5 liters of water. How many liters of water will have leaked when the containers have the same amount of water?

• C.

  Sue had 2 identical pieces of material. She cut off 1.5 feet from one and attached it to the other to create a 6-foot curtain. What was the length, in feet, of each piece of material?

• D.

  Which number on a number line has the property that the distance between the number and 1.5 is the same as the distance between the number's opposite and 6?

Tags

CCSS.6.EE.B.7

The equation below represents a situation.

        2 + 4x = 4.5x

Which word problem could the equation represent?

• A.

  Fernando can swim 4 meters per minute, and Jose can swim 4.5 meters per minute. If they start swimming northward from the same location at the same time, after how many minutes will Jose be 2 meters ahead of Fernando?

• B.

  A certain number of square tiles with sides of length 4.5 inches are used to cover Ronnie's bedroom wall. If the same number of square tiles with sides of length 4 inches are used instead, 2 square inches would be left uncovered. How many tiles with sides of length 4.5 inches cover Ronnie's wall?

• C.

  Marco spends the same amount on movies every week. When the rental per movie is reduced from $4.50 to $4, he can rent 2 extra movies with his usual amount of money. How many movies per week does Marco usually rent?

• D.

  When the people at a party share several boxes of pizza evenly, each gets 4.5 pieces. If there had been 2 boxes fewer, each person would have gotten just 4 pieces. How many people are at the party?

Write an equation that represents the sentence below.

"The product of 14 and x is equal to 28 more than x."

• 14 + x = 28 + x

• 14x = 28 + x

• 14x + x = 28 - x

• 14x = 28 - x

Jamal wants to solve the equation below for x.

9−4x=12x

First, he uses the addition property of equality to add 4x to both sides of the equation. Next, he wants to use the division property of equality. By what number should Jamal divide both sides?

Tags

CCSS.HSA.REI.A.1

Dante read the sentence below in his math homework.

        "The product of 14 and x is equal to 28 more than x."

Which of the following equations represents this sentence?

• A.

  14 + x = 28x

• B.

  14x = 28x

• C.

  14x = 28 + x

• D.

  14 + x = 28 + x

Tags

CCSS.HSA.CED.A.3

Maria wants to buy a trophy and engrave her son's name on it. At Trophies Unlimited, trophies cost $12 each and engraving costs 40¢ per letter, while at Centerpiece Trophies, trophies are $12.50 each and engraving is 30¢ per letter. If Maria's costs would be the same at both stores, which equation shows the number of letters, x, in her son's name?

• A.

  12 + = 12.5 +

• B.

  0.4 + 12x = 0.3 + 12.5x

• C.

  12 + 0.4x = 12.5 + 0.3x

• D.

  12(x + 0.4) = 12.5(x + 0.3)

What is the value of w in the equation 21​w+7=2w−2?

What value of p is the solution of 5p − 1 = 2p + 20?

What is the value of p in the equation 8p + 2 = 4p − 10?