Rick gave his son $100 to buy food and drinks. His son returned with $25.50 in change. Therefore the amount spent was
$100 - $25.50 = $74.50.
Let
x = number of hot dogs bought (at $3.50 per hot dog).
y = number of milk shakes bought (at $8 per milk shake).
There were 8 orders of soda at $5 per soda.
The total order is $74.50, therefore
3.50x + 8y + 8*5 = 74.50
Simplify to obtain
8y = 74.5 - 3.5x
y = 4.3125 - 0.4375x
We must have whole numbers (integers) for x and y.
Create a table that varies x from 0 to 8, and look for y to be an integer, as shown below.
x y
--- -------
0 4.3125
1 3.8750
2 3.4375
3 3
4 2.5625
5 2.1250
6 1.6875
7 1.2500
8 0.8125
Because we cannot have fractional values for either x or y, the solution is x=3, y=3
Answer:
3 hot dogs, 3 milk shakes, and 8 sodas.
