Question

HELPPPPP PLEASEEE

Use the cost tables for two services to create a linear

system of equations. Then solve the system to determine when the cost of

the two services will be equal.

1. The table shows canoe rental prices for two companies.

Timet (in hours) Canoe Depot

Paddle and Oar

$14

1

2

3

$19

$20

$23

$26

$24

2. Two garden supply companies deliver pea stone according to the

following table.

Pea Stone x (in cubic yards) Yard Depot Lawn & Garden

$45

$75

2

$110

$85

3

$145

$125

Answer 1

The cost of the two services will be equal when t = 5/11 hours for the canoe rentals and x = 30/85 cubic yards for the pea stone deliveries.

Explanation:

To create a linear system of equations, we need to first express the cost of each service as a function of time or the amount of pea stone.

For the canoe rentals, let C_1(t) be the cost of renting a canoe from Canoe Depot for t hours and C_2(t) be the cost of renting a canoe from Paddle and Oar for t hours. We can express these functions as follows:

C_1(t) = 14 + 5t

C_2(t) = 19 + 6t

For the pea stone deliveries, let P_1(x) be the cost of ordering x cubic yards of pea stone from Yard Depot and P_2(x) be the cost of ordering x cubic yards of pea stone from Lawn & Garden. We can express these functions as follows:

P_1(x) = 45 + 35x

P_2(x) = 75 + 50x

Now that we have our functions, we can set them equal to each other to find out when the cost of the two services will be equal.

For the canoe rentals, we set C_1(t) = C_2(t) and solve for t:

14 + 5t = 19 + 6t

-5t -6t = 19 - 14

-11t = 5

t = 5/11

For the pea stone deliveries, we set P_1(x) = P_2(x) and solve for x:

45 + 35x = 75 + 50x

-50x - 35x = 75 - 45

-85x = 30

x = 30/85

The cost of the two services will be equal when t = 5/11 hours for the canoe rentals and x = 30/85 cubic yards for the pea stone deliveries.