Question

Angel is trying to decide which parking garage to use. Polite's parking charges a flat fee of $2 plus $4 per hour. Gray's garage charges a flat fee of $8 plus $2 per hour.

For how many hours with the cost of parking in either garage be the same, and what will the cost be?

Answer 1

`\text{Turn the scenarios into equations:}\\\\\text{Polite's parking:}\\\\y=4x+2\\\\\text{Gary's garage:}\\\\y=2x+8\\\\\text{To find when the parking costs the same, solve the expressions together:}\\\\4x+2=2x+8\\\\\text{Solve for x:}\\\\4x+2=2x+8\\\\\text{Subtract 2x from both sides}\\\\2x+2=8\\\\\text{Subtract 2 from both sides}\\\\2x=6\\\\\text{Divide by 2}\\\\x=3\\\\\boxed{\text{In 3 hours, the cost will be the same}}\\\\`

`\text{To find the cost, plug in 3 to x in one of the equations:}\\\\y=4(3)+2\\\\y=12+2\\\\y=14\\\\\boxed{\text{The cost would be \$14}}`