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?

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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?

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Answer 1 · 2018-06-20T05:43:43

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

Explanation:

Let $C_{p}$ $C_p$ represent the calories in the piece of pie,
and $C_{i c}$ $C_(ic)$ 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.
$C_{p} = 3 C_{i c} - 20$ $C_p = 3C_(ic) - 20$

Also from the problem, the calories of both added together is 500:
$C_{p} + C_{i c} = 500$ $C_p + C_(ic) = 500$
$C_{p} = 500 - C_{i c}$ $C_p = 500 - C_(ic)$

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

$C_{i c} = \frac{520}{4} = 130$ $C_(ic) = 520/4 = 130$

Then, we can use this value in any of the equations above to solve for $C_{p}$ $C_p$ :
$C_{p} = 3 C_{i c} - 20$ $C_p = 3C_(ic) - 20$
$C_{p} = 3 \cdot 130 - 20$ $C_p = 3*130 - 20$
$C_{p} = 370$ $C_p = 370$

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

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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?

1 Answer

Explanation:

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