Defining Variables Word Problems

In the 2010 Winter Olympic Games, the United States won 1 more than 4 times the number of gold medals France won. The United States won 7 more gold medals than France.

Write an equation to find the number of gold medals each country won.

• 7 + 4F = F + 1

• 4(7) + F = F + 1

• 7 + F = 4F + 1

• 7F = 4F + 1

Use the equation from #1 to find the number of gold medals each country won.

7 + F = 4F + 1

• France won 2 gold medals and the U.S. won 9 gold medals.

• France won 9 gold medals and the U.S. won 2 gold medals.

• France won 3 gold medals and the U.S. won 10 gold medals.

• France won 13 gold medals and the U.S. won 3 gold medals.

Diego’s sister is twice his age minus 9 years. She is also as old as half the sum of the ages of Diego and both of his 12-year-old twin brothers.

Write an equation to find the ages of Diego and his sister.

• 2d − 9 = (d + 12 + 12)

• Diego is 19 and his sister is 14

• Diego is 14 and his sister is 19

• Diego is 20 and his sister is 14

• Diego is 15 and his sister is 20

The table shows the current heights and average growth rates of two different species of trees. Write an equation to find how long it will take for the two trees to be the same height.

• 38 + x = 45.5 + 2.5x

• 38 + 4x = 45.5 + 2.5x

• 38 + 2.5x = 45.5 + 4x

• 38 + 4x = 45.5 + 2.5y

Use your equation from #5 to find how long it will take for the two trees to be the same height.

38 + 4x = 45.5 + 2.5x

• The two trees will be the same height in 2 years.

• The two trees will be the same height in 3 years.

• The two trees will be the same height in 4 years.

• The two trees will be the same height in 5 years.

A dog weighs two pounds less than three times the weight of a cat. The dog also weighs twenty-two more pounds than the cat.

Write an equation to find the weights of the dog and the cat.

• c − 2 = c + 22

• 3c + 2 = c + 22

• 3c − 2 = c + 22

• 3c − 2 = 22c

Use the equation from #7 to find the weights of the dog and the cat.

3c − 2 = c + 22

• The cat weighs 12 pounds and the dog weighs 34 pounds.

• The cat weighs 34 pounds and the dog weighs 12 pounds.

• The cat weighs 7 pounds and the dog weighs 29 pounds

• The cat and the dog both weigh 12 pounds