Question

The number of calories in a piece of pie is 20 less than 3 times the number of calories in a scoop of ice cream. The pie and ice cream together have 500 calories. How many calories are in each?

Answer 1

The piece of pie has 370 calories while the scoop of ice cream has 130 calories.

Explanation:

Let `C_p` represent the calories in the piece of pie,
and `C_(ic)` represent the calories in the scoop of ice cream

From the problem: The calories of the pie is equal to 3 times the calories of the icecream, minus 20.
`C_p = 3C_(ic) - 20`

Also from the problem, the calories of both added together is 500:
`C_p + C_(ic) = 500`
`C_p = 500 - C_(ic)`

The first and last equation are equal (=`C_p`)
`3C_(ic) - 20 = 500 - C_(ic)`
`4C_(ic) = 520`

`C_(ic) = 520/4 = 130`

Then, we can use this value in any of the equations above to solve for `C_p`:
`C_p = 3C_(ic) - 20`
`C_p = 3*130 - 20`
`C_p = 370`

So, the piece of pie has 370 calories while the scoop of ice cream has 130 calories.