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?

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

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