Three cookies plus two donuts have 400 calories. Two cookies plus three donuts have 425 calories. Find how many calories are in a cookie and how many calories are in a donut?

2 Answers
Feb 23, 2018

Answer:

Calories in a cookie #= 70#
Calories in a donut #= 95#

Explanation:

Let calories in cookies be #x# and let calories in donuts be #y#.

#(3x + 2y = 400) xx 3#

#(2x + 3y = 425) xx (-2)#

We multiply by #3# and #-2# because we want to make the #y# values cancel each other so we can find #x# (this can be done for #x# also).

So we get :

#9x + 6y = 1200#
#-4x - 6y = -850#

Add the two equations so #6y# will cancel

#5x = 350#

#x = 70#

Substitute #x# with #70#

#3(70) +2y = 400#

#2y = 400-210#

#2y = 190#

#y = 95#

Answer:

We need to use simultaneous equations to solve this problem

Explanation:

Let the number of calories in a cookie be #x# and the number of calories in a donut be #y#.

#3x+2y=400" " " "(1)#

#2x+3y=425" " " " (2)#

From #(2)#

#2x=425-3y#

#x=(425-3y)/2" " " "(3)#

Sub #(3)# into #(1)#

#3[(425-3y)/2]+2y=400#

#1275-9y+4y=800#

#-5y=-475#

#y=95" " " "(4)#

Sub #(4)# into #(1)#

#3x+2(95)=400#

#x=70#

Therefore, each cookie has #70# calories and each donut has #95# calories.