SOLUTION: Hello: The method suggested to solve this is by solving backwards. How would I go about doing this? Harold loves to eat cookies. He eats 1/4 of the package on Monday. On Tue

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Hello: The method suggested to solve this is by solving backwards. How would I go about doing this? Harold loves to eat cookies. He eats 1/4 of the package on Monday. On Tue      Log On


   

Question 1160292: Hello:
The method suggested to solve this is by solving backwards. How would I go about doing this?
Harold loves to eat cookies. He eats 1/4 of the package on Monday. On Tuesday, he eats 13 cookies. On Wednesday, he eats 1/2 as many as he did on Monday. If there are 22 cookies left in the package on Thursday, how many cookies did he start with?
Thanks for your help.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let number of cookies be x
given:
He eats 1%2F4 of the package on Monday
On Tuesday, he eats 13 cookies.
On Wednesday, he eats 1%2F2 as many as he did on Monday=> %281%2F4%29%2F2=1%2F8

so he ate:
%281%2F4%29x%2B13%2B%281%2F8%29x
. If there are 22+cookies left in the package on Thursday, ->x-22
then we have
%281%2F4%29x%2B13%2B%281%2F8%29x=x-22
%281%2F4%29x%2B13%2B%281%2F8%29x%2B22=x......both sides multiply by 8
2x%2B104%2B+x%2B176=8x
280=8x-3x
5x=280
x=56

he start with x=56 cookies
check:
he eats %281%2F4%29x=56%2F4=14 on Monday
he eats 13 cookies on Tuesday
he eats %281%2F8%29x=56%2F8=7 on Wednesday
there are 22+cookies left in the package on Thursday
add all together:
14%2B13%2B7%2B22=56
56=56