Mrs. Boyd went shopping at city center Mall. she parked her car in the parking garage. The cost for parking was $1.00 for the first hour and $0.75 for each additional 1/2 hour. Mrs. Boyd paid $4.75 for parking. Write an equation to find how long Mrs. Boyd was shopping. How long did she shop? Explain how you arrived at your equation and show your work to solve your equation.
Can someone please help me with this problem?
She shopped for 3 1/2 hours.
If you write the equation and explain it, we'll be glad to check it.
Since he paid more than $1, he must have parked more than one hour. Let T be the number of hours parked. T-1 is the number of hours parked at the lower rate.
Your equation is:
4.75 = 1.0 + 0.75*2*(T-1)
which can be rewritten as
4.75 = 1 + 1.5 (T-1)
The "2" gets multiplied in because they charge by the half hour after one hour.
Solve that equation for T.
Sure! We can solve this problem by first setting up an equation to represent the cost of parking based on the amount of time Mrs. Boyd spent shopping. Let's break it down step by step.
Let's assume that Mrs. Boyd spent a certain number of hours, h, shopping. We need to find the number of additional half-hours she spent, so we can represent it as 2x.
The equation to find the total cost of parking is:
Cost = 1 + 0.75x
Given that Mrs. Boyd paid $4.75 for parking, we can set up the equation:
4.75 = 1 + 0.75x
To solve for x, we'll subtract 1 from both sides:
4.75 - 1 = 1 + 0.75x - 1
3.75 = 0.75x
Now, divide both sides by 0.75 to isolate x:
x = 3.75 / 0.75
x = 5
So, Mrs. Boyd spent 5 additional half-hours shopping. To find how long she shopped in total, we need to calculate the number of hours corresponding to these additional half-hours. Since each additional half-hour corresponds to half of an hour, we can divide x by 2 to get the number of hours:
hours = x / 2 = 5 / 2 = 2.5
Therefore, Mrs. Boyd shopped for 2.5 hours.