Question

A vending machine sells chips at $0.65 and candy at $0.75. Last month, the vending machine yielded $243.80 with the sale of 350 items.
Let x be the number of chips sold and y the number of candies. How many packages of chips were purchase last month?

Answer 1

The first thing we need to do is to assign variables. Let $x$ represent the number of chips sold and let $y$ represent the number of candies sold. Now we can write two equations.

$0.65x+0.75y=243.80$
$x+y=350$

Let's simplify our first equation by multiplying the whole equation by 100.

$65x+75y=24380$

We can solve for $x$ in the second equation and we get $x=350-y$.

Now we can substitute the value of $x$ into the first equation.

$65(350-y)+75y=24380$
$22750-65y+75y=24380$
$22750+10y=24380$
$10y=1630$
$y=163$

Now we can substitute the value of $y$ into the second equation.

$x+163=350$
$x=187$

Therefore the number of chips sold is 187.