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?
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"Question #23ae1"
Calories in a cookie #= 70#
Calories in a donut #= 95#
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#
We need to use simultaneous equations to solve this problem
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.
