Question

6). To make trail mix you need 2

cups of raisins for every 3 cups
of almonds. How many cups of
raisins are needed for 12
cups of almonds?

Answer 1

`\boxed {\boxed {\sf 8 \ cups \ of \ raisins }}`

Explanation

Let's create a proportion using this setup.

`(raisins)/(almonds) =(raisins)/(almonds)`

We know that 2 cups of raisins are needed for 3 cups of almonds.

`(2 \ cups \ raisins)/(3 \ cups \ almonds) =(raisins)/(almonds)`

We don't know how many cups of raisins are needed for 12 cups of almonds. Therefore, x cups of raisins are needed for 12 cups of almonds.

`(2 \ cups \ raisins)/(3 \ cups \ almonds) =(x \ cups \ raisins)/(12 \ cups \ almonds)`

`(2 )/(3) =(x )/(12 )`

Since we are solving for x, we must isolate that variable. It is being divided by 12. The inverse operation of division is multiplication. Multiply both sides of the proportion by 12.

`12*(2 )/(3) =(x )/(12 )*12`

`12*(2 )/(3)=x`

`8=x`

8 cups of raisins are required for 12 cups of almonds.