Question

A delivery service offers two package sizes. On Monday, the service delivered 40 large and 20 small packages for a cost of $380. On Tuesday, 32 large and 80 small packages were delivered for $496.Based on the graph for Monday and Tuesday, which is closest to the cost to deliver each type of package?

Answer 1

The closest cost to deliver a large package is $8, and the cost to deliver a small package is $3. This was determined by setting up and solving a system of equations based on the given delivery data for Monday and Tuesday.

Step-by-step explanation:

To find the closest cost to deliver each type of package, we need to set up a system of equations based on the data given for Monday and Tuesday's deliveries. Let's assign variables to the cost of delivering a large and a small package:

• Let L be the cost to deliver a large package.
• Let S be the cost to deliver a small package.

Using the delivery data, we can develop the following equations:

1. 40L + 20S = 380 (Monday's deliveries)
2. 32L + 80S = 496 (Tuesday's deliveries)

Now we can solve this system of equations using the substitution or elimination method. Let's use the elimination method:

1. Multiply the first equation by 4 and the second by 1 to get the coefficients of S the same:
2. 160L + 80S = 1520
3. 32L + 80S = 496
4. Subtract the second equation from the first:
5. (160L + 80S) - (32L + 80S) = 1520 - 496
6. 128L = 1024
7. Divide both sides by 128 to get the cost of a large package:
8. L = 1024 / 128
9. L = 8
10. Now plug the value of L into one of the original equations to solve for S:
11. 40(8) + 20S = 380
12. 320 + 20S = 380
13. 20S = 380 - 320
14. 20S = 60
15. Divide both sides by 20 to get the cost of a small package:
16. S = 60 / 20
17. S = 3

Therefore, the closest cost to deliver a large package is $8 and a small package is $3.