Question 301362: A vending machine sells chips at $0.40 and candy at $0.50. Last month, the vending machine yielded $139.80 with the sale of 298 items.
let x be the number of chips sold and y the number of candies. How many packages of chips were purchased last month?
Answer by lukechalfant(2)   (Show Source):
You can put this solution on YOUR website! To solve this one use a system of equations.
First, you know that the total number of items sold was 298.
If x is the number of chips and y is the number of candies, then:
x + y = 298
Now, you don't know how many chips were sold but you know their cost: $0.40
If x is the number of chips sold than .4(x) = the total sales of chips.
Do this with the candy as well: .5(y)
You also know that the total profit was $139.80. So:
.4(x) + .5(y) = 139.8
(it makes it easier for me to drop off the zeros, you can keep them on if you want to)
Now multiply the second equation by 10 to get rid of decimals.
So here are the two equations:
x + y = 298
4(x) + 5(y) = 1398
To solve this there are a few ways. I can't remember the name of this method but the general idea is to make one variable opposite in one equation of what it is in the other. Like 4x and -4x. To get the first equation to have a -4x multiply the entire equation by -4. Then use this with the other equation to cancel out x. Think of it vertically in columns and simplify down, like this:
-4x + -4y = -1192
4x + 5y = 1398
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0x + y = 206
So y = 206
Going back to one of the first equations and plugging in the new found y you get:
x + 206 = 298
- 206 -206
x = 92
So they sold 206 candies and 92 bags of chips.
To check, does 206 + 92 = 298? It does. Does 4(92) + 5(206) = 1398? It does.
92 bags of chips is the answer.
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