SOLUTION: I need to know how to set up this equation. Please explain the logic behind how you set it up. A purse contains $3.75 in 5 cent and 20 cent coins. there are 33 coins all together.

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Question 874334: I need to know how to set up this equation. Please explain the logic behind how you set it up. A purse contains $3.75 in 5 cent and 20 cent coins. there are 33 coins all together. How much of each coin is there?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
A purse contains $3.75 in 5 cent and 20 cent coins. there are 33 coins all together. How much of each coin is there?
.
Let x = number of 5 cent coins
and y = number of 20 cent coins
then
from "A purse contains $3.75" we get:
.05x + .20y = 3.75 (equation 1)
and from "there are 33 coins" we get:
x + y = 33 (equation 2)
.
Solve equation 2 for y:
x + y = 33
y = 33-x
.
Substitute above into equation 1 and solve for x:
.05x + .20y = 3.75
.05x + .20(33-x) = 3.75
.05x + 6.60 - .20x = 3.75
6.60 - .15x = 3.75
-.15x = -2.85
x = -2.85/(-.15)
x = 19 (number of 5 cent coins)
.
number of 20 cent coins:
y = 33-x = 33-19 = 14