Question

Marty has a box of raisins. He uses 1 1/2 cups of raisins for trail mix. Then he opens a bag with 2 1/3 cups of raisins in it. Marty then uses 3/4 cup of raisins for bread pudding. There are 3 1/2 cups of raisins left. How many cups of raisins were in the box. Explain.

Answer 1

Explanation:

x=box raisins

Total raisins = raisins used plus raisins left

x+7/3 = 3/2+3/4+7/2

x-7/3+7/3 = 3/2+7/2+3/4-7/3

x = 10/2 + 3/4 - 7/3

Find GCF

x = 6/6*10/2 + 3/3*3/4 - 4/4*7/3

x = 60/12 + 9/12 - 28/12

x = 69/12 - 28/12

x = 41/12

x = 3-5/12 cups raisins in the box

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Answer 2

`5(3)/(4)\ cups\ of\ raisins`

Explanation:

Let

x------> cups of raisins originally in the box

we know that

The original quantity is equal to the quantity that is left plus the quantity used

so

`x=3(1)/(2)+ 1(1)/(2)+(3)/(4)`

Convert mixed number to an improper fraction

`3(1)/(2)=(3*2+1)/(2)=(7)/(2)`

`1(1)/(2)=(1*2+1)/(2)=(3)/(2)`

substitute

`x=(7)/(2)+ (3)/(2)+(3)/(4)`

`x=(10)/(2)+ (3)/(4)`

`x=5+ (3)/(4)`

`x=5(3)/(4)\ cups\ of\ raisins`