http://www.weekofgeek.com/video-game-rental-cost-3/
Video Game Rental Cost
I couldn't get to the right solution with this question, please help?
Ken asked a friend to rent him a video game and as a joke the friend rented one that he didn’t think Ken would like. He was right. So Ken paid his friend the rental cost of $6.15 (including taxes) but he paid him using only nickels ($0.05) and dimes ($0.10). If there were 3 more dimes than nickels, how many of each coin did Ken give his friend?
The solution should be written in a linear equation form.
I will start by saying:
let x= the number of dimes
let y= the number of nickels.
here is the equation in case you need it.
x+y= 6.15
0.05y= 0.10x-3 << i seem to be stuck somewhere in the solution. thnx in advance.
let x= the number of dimes paid.
let y= the number of nickels paid.
We know that the number of dimes paid was 3 more than the number of nickels paid.
x = y + 3
The amount paid in dimes is 0.10x.
The amount paid in nickels is 0.05y.
The total paid is equal to the amount paid in dimes and nickels.
6.15 = 0.1x + 0.05y
We now have a system of 2 equations.
x = y + 3
6.15 = 0.1x + 0.05y
We next solve both for y, since we need linear equation forms.
x = y + 3
y + 3 = x
y = x - 3
6.15 = 0.1x + 0.05y
0.05y + 0.1x = 6.15
5y + 10x = 615
y + 2x = 123
y = -2x + 123
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We now have a system of 2 equations, both of which could be graphed as lines since they are in linear equation form.
y = x - 3
y = -2x + 123
That's as far as you can go if you are limited to the answer being in linear equation form. The next step would be to graph both lines and find the intersection (if any). That point, it's x and y values, would be the solution.
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PS: I will solve it anyway.
y = x - 3
y = -2x + 123
y = y
Therefore:
x - 3 = -2x + 123
(x - 3) + 2x = (-2x + 123) + 2x
3x - 3 = 123
3x = 126
x = 42
So 42 dimes were paid.
y = x - 3
y = 42 - 3
y = 39
So 39 nickels were paid.
The solution is (42, 39)
42 dimes and 39 nickels were paid.
CHECK:
(42 * 0.10) + (39 * 0.05) = 6.15
4.2 + 1.95 = 6.15
6.15 = 6.15
