Question 1131748: During a fundraiser, you will be trying to sell three types of candy. Chocolate bars are $3 each, nutty bars are $2.50 each, and caramel chocolate bars cost $4 each. You sell a total of 1,000 bars and collect $3,225. The number of caramel chocolate bars sold was 100 less than twice the number chocolate bars. Find the number of each type of candy bar that was sold
Please help me with setting up 3 equations
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! During a fundraiser, you will be trying to sell three types of candy.
a,b,c; chocolate, nutty, caramel Choc
:
Chocolate bars are $3 each, nutty bars are $2.50 each, and caramel chocolate bars cost $4 each.
You sell a total of 1,000 bars and collect $3,225.
a + b + c = 1000
and
3a + 2.5b + 4c = 3225
:
The number of caramel chocolate bars sold was 100 less than twice the number chocolate bars.
c = 2a - 100
or
2a - c = 100
:
Find the number of each type of candy bar that was sold.
:
Use the first two equations to eliminate b
multiply the 2nd equation by 2, multiply the first equation by 5
6a + 5b + 8c = 6450
5a + 5b + 5c = 5000
-------------------------subtraction eliminates b
a + 0 + 3c = 1450
:
multiply the 3rd equation by 3, pair with the above equation
6a -3c = 300
a + 3c = 1450
----------------adding eliminates c, find a
7a + 0 = 1750
a = 1750/7
a = 250 Chocolates sold
:
:
I'll let you find b and c, check your solutions in all three equations
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