SOLUTION: A friend spent $19.5 on buying candy. Lollipops cost $0.32 and Hershey kisses cost $0.23 each. If she bought 75 pieces of candy, how many of each type did she buy?

Question 1195959: A friend spent $19.5 on buying candy. Lollipops cost $0.32 and Hershey kisses cost $0.23
each. If she bought 75 pieces of candy, how many of each type did she buy?
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your two equations are:
.32x + .23y = 19.5
x + y = 75
x is the number of lollipops.
y is the number of hershey kisses.
these are two equations that need to be solved simultaneously.
one way is as follows:
multiply both sides of the second equation by .32 and leave the first equation as is to get:
.32x + .23y = 19.5
.32x + .32y = 24
subtract the first equation from the second to get:
.09y = 4.5
solve for y to get:
y = 4.5/.09 = 50
this makes x = 25 because 25 + 50 = 75
confirm by taking .32 * 25 + .23 * 50 = 19.5
your solution is 25 lollipops and 50 hersey kisses are bought.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The other tutor showed a solution using a standard formal algebraic method.

A very different method can be used on any 2-part "mixture" problem like this which can make it easier to find the answer if the numbers are "nice".

In this problem, one kind of candy costs $0.32 each and another costs $0.23 each; and 75 pieces of candy cost $19.50.

Divide the $19.50 by 75 to find the average cost of the pieces of candy is $0.26.

Then, seeing that $0.26 is 1/3 of the way from $0.23 to $0.32, we know that 1/3 of the candies are the more expensive ones. So 75/3 = 25 of the candies are lollipops, leaving 50 for the number of kisses.

ANSWER: 25 lollipops, 50 kisses

CHECK: 25(0.32)+50(0.23)=8.00+11.50 = 19.50

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