There are 48 more chicken nuggets than fish nuggets on the plate. After some cildren ate 12 chicken nuggets and 12 fish nuggets there were 3 times as many chicken nuggets as fish nuggets. How many nuggets were there on the plate?
Let there be 'c' chicken nuggets and 'f' fish nuggets
There are 48 more chicken nuggets than fish nuggets on the plate.
c = f + 48 ...(1)
After some children ate 12 chicken nuggets and 12 fish nuggets there were 3 times as many chicken nuggets as fish nuggets.
c-12 = 3(f-12)
=> c = 3f - 24 ...(2)
Substitute (1) into (2) to find f:
f = ___ ...(3)
Substitute (3) into (1) to find c:
c = ___ ...(4)
How many nuggets were there on the plate?
Add (3) and (4):
.: c + f = ___
fish nuggets --- f
chicken nuggets --- f+48
after "eating"
fish nuggets = f-12
chicken nuggets = f+48 - 12 = f+36
" there were 3 times as many chicken nuggets as fish nuggets" ---> f+36 = 3(f-12)
f+36 = 3f - 36
-2f = -72
f = 36
so they started with 36 fish nuggets and 84 chicken nuggets
check:
were the 48 more chicken than fish ? YES
after eating:
fish -- 36-12 = 24
chichen -- 84-12 = 72
3 times as many chicken as fish ? YES
To solve this problem, let's break it down step by step.
1. Let's assume the number of fish nuggets on the plate is "x".
Thus, the number of chicken nuggets on the plate would be "x + 48" (since there are 48 more chicken nuggets than fish nuggets).
2. After some children ate 12 chicken nuggets and 12 fish nuggets, we subtract these amounts from their respective totals:
Remaining chicken nuggets = (x + 48) - 12
Remaining fish nuggets = x - 12
3. According to the problem statement, the remaining chicken nuggets were three times the number of remaining fish nuggets:
(x + 48) - 12 = 3 * (x - 12)
Solving this equation will give us the value of x, which represents the original number of fish nuggets on the plate.
4. Once we find x, we can find the total number of nuggets on the plate by adding the number of chicken and fish nuggets:
Total nuggets = (x + 48) + x
Let's solve the equation and find the answer.