Melillo Middle School prepared 30 cups of trail mix for a carnival. The ratio of nuts to dried fruit in the trail mix was 3 to 2. If the teachers ate 6 cups of nuts out of the mix, how many cups of dried fruit would need to be taken out in order to keep the original ratio?

Ratio is 3:2

30 total

3+2=5

30=5 units

divide by 5

6=1 unit

at first there is

3 (6) : 2 (6) = 18:12

18 nuts and 12 dried fruit

if teachers ate 6 nunts then hoa much fruit must be taken out to keep it same

18-6=12

12:x=3:2

treat as fraction

12/x=3/2

multiply both sides by x to clear x

12=3x/2

multiply both sides by 2 to cleaer fraction

24=3x

divide by 3

8=x

it needs to be 8

12-x=8

subtract 12 from both sides

-x=-4

multiply - 1

x=4

4 cups must be taken out

4 cups of dried fruit would need to be taken out to keep the original ratio.

Given:

30 cups of trail mix.

ratio of nuts to dried fruit is 3 to 2.

3:2 = 6:x

3x = 2*6

3x = 12

3x/3 = 12/3

x = 4 cups of dried fruits