This question is about how to write a linear equation.

Question

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

Answer 1

This equation uses 2 variables - how do we know what our variables should be? Our hint here is what the question asks for at the end… the number of bike rentals and the number of skate rentals.

 

Let's name our variables

b=number of bike rentals

s=number of skate rentals

 

We have two variables, so we'll need two equations to be able to solve. 

 

The first one we write will use the total number of rentals (20). The total number of rentals is really just the sum of the number of bike rentals and the number of skate rentals.

 

b+s=20

 

The second equation uses the total revenue for the day ($455 - how much the business made). Revenue is equal to the number of goods sold multiplied by the price of goods sold (if you buy 3 ice cream bars for $2 each, you would multiply the number of bars, 3, by the price per bar, $2, to get $6 total) . In this situation we have two different types of goods, so we'll need to take advantage of our variables.

 

25b+20s=455

 

Now let's look at our two equations together

 

b+s=20

25b+20s=455

 

There are many ways to solve this, but in whatever method you choose, you will need to solve for one variable and then plug back in to get the other.

 

I would isolate a variable in the first equation

 

b=20-s

 

and plug into the second equation to solve

 

25(20-s)+20s=455

500-25s+20s=455

500-5s=455

45=5s

9=s

 

You can then plug the result back into one of the original equations to find b

 

b+s=20

b+9=20

b=11

 

11 bike rentals and 9 skate rentals.

 

Now to double check

 

11 bike rentals at $25 each = $275

9 skate rentals at $20 each = $180

 

$275+$180=$455