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
Jun 20, 2018

Answer:

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.