A business rents bicycles and in-line skates. Bicycle rentals cost $25 per day, and in-line skate rentals cost $20 per day. The business has 20 rentals today and makes $455. (Section 5.3) a. Write a system of linear equations that represents this situation. b. How many bicycle rentals and in-line skate rentals did the business have today

a.

25 b+20 s=455 ... equation 1

b+s=20 ... equation 2, where b and s are the number of bicycle and in-line skate rentals per day.

b. The business had 11 bicycle rentals and 9 in-line skate rentals.

Explanation:

a.

Step 1: Determine an equation for total revenue today

Since the business rents bicycles and in-line skates, the total revenue will be as a result of amount received in revenue from renting the bicycles and in-line skates. This can be expressed as shown;

T = (B*b) + (S*s)

where;

T=total revenue

B=bicycle rental cost per day

b=number of bicycles

S=in-line skate rental cost per day

s=number of in-line skates

In our case;

T=$455

B=$25 per day

b=unknown

S=$20 per day

s=unknown

Replacing;

(25*b) + (20*s) = 455

25 b+20 s=455 ... equation 1

Step 2: Determine an equation for total rentals today

The equation for the total number of rentals is;

R=b+s

where;

R=total number of rentals today

b=number of bicycles

s=number of in-line skates

In our case;

R=20

b=unknown

s=unknown

Replacing;

b+s=20 ... equation 2

b.

Step 3: Combine equation 1 and 2 ans solve simultaneously

1 (25 b+20 s=455), multiplying equation 1 by 1=25 b+20 s=455

20 (b+s=20), multiply equation 2 by 20=20 b+20 s=400

25 b+20 s=455

-

20 b+20 s=400

5 b+0 s=55

(5 b) / 5=55/5=11

b=11, replace the value for b in equation 2 and solve;

(20*11) + 20 s=400

220+20 s=400

20 s=400-220=180

20 s=180

s = (180/20) = 9

The business had 11 bicycle rentals and 9 in-line skate rentals.