Question

Aldrine is buying coffee for his coworkers. He orders small and large coffees. Small coffees

cost $3 and large coffees cost $5. He spent $30 and ordered eight cups of coffee in total.
Write a system of equations that represents the situation
How many of each coffee did he buy? How do you know?

Answer 1

Let small cups = S

Large cups = L

They bought a total of 8 cups, so S + L = 8

Rewrite as S = 8-L (1st equation)

Then you also have

$3S + $5L = $30 (2nd equation)

Replace the S in the second equation with the first equation:

$3(8-L) + $5L = $30

Simplify:

24 - 3L + 5L = 30

Combine like terms:

24+2L = 30

Subtract 24 from both sides:

2L = 6

Divide both sides by 2:

L = 3

They bought 3 large cups

Since they bought a total of 8 cups, that means they bought 5 small cups ( 8-3=5)

Large = 3 cups, Small = 5 cups