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lara31 [8.8K]
2 years ago
7

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
Business
1 answer:
Alja [10]2 years ago
8 0

Answer:

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.

<em>Step 1: Determine an equation for total revenue today</em>

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

<em>Step 2: Determine an equation for total rentals today</em>

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.

<em>Step 3: Combine equation 1 and 2 ans solve simultaneously</em>

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.

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