An online book company offers different shipping rates for different delivery options. The equations shown below can be used to calculate the total shipping cost, C, for a delivery of x number of books.
| Delivery Option | Total Cost Equation |
| 3 - 5 business days | C = 3 + 0.99x |
| Within 2 business days | C = 9.99 + 1.99x |
Alisha ordered 5 books from the company. How much money does she save, in dollars, if she chooses the first delivery option over the second?
- Read and understand the situation.
The problem gives two delivery option equations; the first is for 3-5 business days and the second is within 2 business days. Given that Alisha ordered 5 books, we want to determine how much money she will save if she chooses the longer delivery option. Is it worth it for Alisha to wait a little longer for her books?
- Identify and pull out important information from the problem.
We were given the two equations in this problem.
| Delivery Option | Total Cost Equation |
| 3 - 5 business days | C = 3 + 0.99x |
| Within 2 business days | C = 9.99 + 1.99x |
We want to know how much money Alisha will save by ordering five books using the first delivery option rather than the second
- Assign variables to unknown values.
C = cost of delivery
x = number of books. In this problem, x = 5.
Using the table will help us to organize the two different costs we are comparing.
- Set up and solve the equation.
Let's expand our table to organize the equations.
| Delivery Option |
Total Cost Equation |
Total Cost for
Five Books |
Simplified Cost Equations |
| 3 - 5 business days |
C = 3 + 0.99x |
C = 3.00 + 0.99(5) |
C = 3.00 + 0.99(5)
C = 3 + 4.95
C = 7.95
|
| Within 2 business days |
C = 9.99 + 1.99x |
C = 9.99 + 1.99(5) |
C = 9.99 + 1.99(5)
C = 9.99 + 9.95
C = 19.94
|
The cost for 5 books to be delivered in 3-5 days is $7.95 and the cost for delivery of 5 books within 2 days is $19.94. What is the difference between the two?
Just subtract!
The difference between the two delivery options is $19.94 – $7.95, which is $11.99.
- Check that your answer makes sense within the context of the problem.
If Alisha can wait 3-5 days for her books rather than getting them within 2 days, she will save $11.99. Is it worth it for her to wait? You decide!
Luca's drive to college includes a 260-mile stretch on an interstate highway and at least one hour of driving time off the highway. The maximum speed limit on the highway is 65 miles per hour. The equation below shows the relationship between distance, speed, and time.
Distance = Speed x Time
Assuming Luca drives at a constant speed that is not over the speed limit on the highway, what is Luca's minimum driving time, in hours? Remember to follow our problem solving steps!
Step 1: Read and understand the situation.
Luca is driving a total of 260 miles on the highway to college. She will drive on the highway for the full 260 miles and off of the highway for one more hour. The problem wants the minimum amount of time it will take her to get there.
Step 2: Identify and pull out important information from the problem.
Total miles to drive on the highway: 260 miles
Maximum speed on the highway: 65 miles per hour
The problem states that she will drive at a constant speed that does not exceed the maximum highway speed, so the fastest she can go the whole time on the highway is 65 miles per hour. The problem also states that she will drive for one additional hour off of the highway.
Step 3: Assign variables to unknown values.
It is not known how much time it will take her to get there, except that she will drive one hour off of the highway. We will use t for time on the highway,
t = the minimum amount of time it will take Luca to drive 260 miles on the highway
We will add one hour to t after solving the equation.
Step 4: Set up and solve the equation.
We will use the distance formula that we were provided: Distance = Speed x Time. Since she will drive 260 miles at 65 miles per hour, we have 260 equals 65 times the number of hours.
260 = 65t
65t = 260 Divide both sides of the equation by 65
t = 4
Step 5: Check that your answer makes sense within the context of the problem.
First, we must check our answer to the equation to be sure that we solved it correctly.
65t = 260
65(4) = 260
260 = 260
The minimum amount of time that Luca drives on the highway requires that she drive at the maximum speed. Therefore, the minimum time she will drive on the highway is 4 hours. She will drive off of the highway for one hour for a total of 4 + 1 = 5 hours.
