My father owned a gas station. He generally didn't have much use for math beyond arithmetic, but he once asked me a similar question. Dean, he said, I changed the price of regular gas today from 119.99 to 123.99 (cents per gallon). According to the pump we pumped 1700 gallons exactly for a revenue of $2058.03. How much gas did we sell at each price?
I was happy to solve this math problem for him and I'm happy to solve it for you.
Define your variables
x = # adult tickets, y = # children tickets
Create a system of equations:
He sold 20 tickets, so we write the equation:
x + y = 20
He made $210 selling adult tickets for $12 and children tickets for $6:
210 = 12x + 6y
Solve the system
We multiply the first equation by 6.
120 = 6x + 6y
We subtract from the second equation,
90 = 6x
x = 90/6 = 15
y = 20 - x = 5
Answer: Sold 15 adult tickets, 5 children tickets
They left out an important part:
Check
15 + 5 = 20, good
12(15) +6(5) = 180 + 30 = 210, good
