A vending machine sells chips at $0.55 and candy at $0.75. Last month, the
vending machine yielded $189.00 with the sale of 280 items.
Let x be the number of chips sold and y the number of candies. How many packages
of chips were purchased last month?
Let the number of chips be x
Let the number of candies be y
Value Value
Type Number of of
of of EACH ALL
item items item items
-------------------------------------------
chips x $0.55 $0.55x
candies y $0.75 $0.75y
-------------------------------------------
TOTALS 280 ----- $1890
The first equation comes from the second column.
x + y = 280
0.55x + 0.75y = 1890
Get rid of decimals by multiplying every term by 100:
55x + 75y = 18900
So we have the system of equations:
.
We solve by substitution. Solve the first equation for y:
x + y = 280
y = 280 - x
Substitute (280 - x) for y in 55x + 75y = 18900
55x + 75(280 - x) = 18900
55x + 21000 - 75x = 18900
-20x + 21000 = 18900
-20x = -2100
x = 105 = the number of chips.
Substitute in y = 280 - x
y = 280 - (105)
y = 175 candies.
The number of candies is 280-x or 280-105 or 175 candies.
Checking: 105 chips is $0.55*105 = $57.75 and
175 candies is $0.75*175 = $131.25
That's 280 items.
And indeed $57.75 + $131.25 = $189.00
Edwin