Question 640123: if i had one dollar and i brought 100 pieces of candy, some at 5 cent each and some at 2 cent each and some at 10 for 1 cents , so how many pieces of candy did i purchase at each cent.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! If I had one dollar and I brought 100 pieces of candy;
some at 5 cent each, and some at 2 cent each, and some at 10 for 1 cents,
How many pieces of candy did I purchase at each cent.
:
Let x = no. of 5 cent candies
Let y = no. of 2 cent candies
Let z = no. of 10 for 1 cent
:
x + y + z = 100 candies
:
5x + 2y + .1z = 100 cents
We have 3 unknowns and two equations, but we know 10 for one cent,
candies has to be a multiple of 10, and <100
:
Let z = 70 candies
x + y + 70 = 100
x + y = 30; subtracted 70 from both sides
then
5x + 2y + .1(70) = 100
5x + 2y + 7 = 100
5x + 2y = 93; subtracted 7 from both sides
:
Multiply the 1st equation by 2, subtract from the above equation
5x + 2y = 93
2x + 2y = 60
-------------- subtraction eliminates y, find x
3x = 33
x = 11 ea 5 cent candies
:
Find y
x + y + z = 100
11 + y + 70 = 100
y = 100 - 81
y = 19 ea 2 cent candies
:
:
See if that works
5(11) + 2(19) + .1(70) =
55 + 38 + 7 = 100 cents
:
Summarize
11 ea 5 cent candies
19 ea 2 cent candies
70 ea 10/1 cent candies
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