Writing Equations from Word Problems

Writing Equations from Word Problems

Multiple Choice

If four times a number is increased by 15, then the result is three less than six times the number. Which equation can be used to find the value of the number?

• 4x + 15 = 6(x − 3)

• 4(x + 15) = 6x − 3

• 4x + 15 = 6x − 3

• 4x + 15 = 3 − 6x

Multiple Choice

If five times a number is subtracted from 27, the result is nine more than four times the number. Which equation can be used to find the value of the number?

• 5(27 - x) = 9 + 4x

• 27 - 5x = 4(9 + x)

• 27 - 5x = 4x + 9

• 5x - 27 = 9 + 4x

Multiple Choice

A number m increased by 23 is equal to 15 more than twice the number m.

• m + 23 = m + 15

• m + 23 = m² + 15

• m + 23 = 2m + 15

• m + 23 = 2(m + 15)

Multiple Choice

The equation below represents a situation.

40x = 1,000 + 0.30x Which word problem could the equation represent?

• Calculators cost $40 each at Tech Central. How many calculators can Mrs. Robinson buy for her class with $1,000 if the tax on each calculator is 30¢?

• Ivan deposits $1,000 in an account that earns interest at a rate of 30¢ per $1,000 per year. If he withdraws $40 every year, after how many years will his account be empty?

• Hyun owes Pablo $1,000, and his debt increases by 30¢ each day. If he saves $40 per day, after how many days will he be able to pay off his debt?

• Ada plans to give to charity $300 of every $1,000 she raises at a fundraiser. If she raises only $40, how much will she give to charity?

Multiple Choice

The equation below represents a situation.

2 + 4x = 4.5x Which word problem could the equation represent?

• 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 sametime, after how many minutes will Jose be 2 meters ahead of Fernando?

• 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?

• 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?

• 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?

Multiple Choice

The equation below represents a situation.

x − 1.5 = 6 − x Which word problem could the equation represent?

• 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?

• 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?

• 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?

• 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?