# 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?

Jun 20, 2018

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 ${C}_{i c}$ 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.
${C}_{p} = 3 {C}_{i c} - 20$

Also from the problem, the calories of both added together is 500:
${C}_{p} + {C}_{i c} = 500$
${C}_{p} = 500 - {C}_{i c}$

The first and last equation are equal (=${C}_{p}$)
$3 {C}_{i c} - 20 = 500 - {C}_{i c}$
$4 {C}_{i c} = 520$

${C}_{i c} = \frac{520}{4} = 130$

Then, we can use this value in any of the equations above to solve for ${C}_{p}$:
${C}_{p} = 3 {C}_{i c} - 20$
${C}_{p} = 3 \cdot 130 - 20$
${C}_{p} = 370$

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