SOLUTION: A teacher must buy 100 treats for exactly $100. Chocolate costs $0.56 each, cupcakes cost $0.92 each, and large cakes cost $2.26 each. How many of each does she buy to have a tot

Question 581274: A teacher must buy 100 treats for exactly $100. Chocolate costs $0.56 each, cupcakes cost $0.92 each, and large cakes cost $2.26 each. How many of each does she buy to have a total of 100 for $100?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A teacher must buy 100 treats for exactly $100.
Chocolate costs $0.56 each, cupcakes cost $0.92 each, and large cakes cost $2.26 each.
How many of each does she buy to have a total of 100 for $100?
:
we got 3 unknowns, and only two equations, calls for some help from our calc
:
Let a = no. of Chocolates
Let b = no. of cupcakes
Let c = no. of large cakes
:
a + b + c = 100
:
.56a + .92b + 2.26c = 100.00
multiply by 100 to get rid of the decimals
56a + 92b + 226c = 10000
:
Multiply the 1st equation by 56, subtract from the above equation
56a + 92b + 226c = 10000
56a + 56b + 56c = 5600
----------------------------subtraction eliminates a
0a + 36b + 170c = 4400
36b = -170c + 4400
divide by 36, reduce the fractions
b = c +
:
Only one integer solution for this equation (used the table on a Ti83)
c = 10 cakes
b = 75 cupcakes
then
a = 100 - 85
a = 15 chocolate
:
See if this checks out by finding total cost
.56(15) = 8.40
.92(75) = 69.00
2.26(10)= 22.60
-----------------
total$ = $100.00
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