Question

A company that offers tubing trips down a river rents tubes for a person to use and "cooler" tubes to carry food and water. A group spends $270 to rent a total of 15 tubes. Write a system of linear equations that represents this situation. How many of each type of tube does the group rent? Person tube $20 Cooler tube $12.50

Answer 1

• The number of one-person tubes rented = 11

• The number of cooler tubes rented = 4

• System of linear equations : x + y = 15 , 20x + 12.50y = 270

Correct question : A company that offers tubing trips down a river rents tubes for a person to use and “cooler” tubes to carry food and water. A group spends $270 to rent a total of 15 tubes. Write a system of linear equations that represents this situation. Use x to represent the number of one-person tubes rented and y to represent the number of cooler tubes rented. a one person tube costs $20 and a cooler tube costs $12.50 How many of each type of tube does the group rent? what are the two system of equations?

Given :

• A company that offers tubing trips down a river rents tubes for a person to use and “cooler” tubes to carry food and water.

• A group spends $270 to rent a total of 15 tubes. Write a system of linear equations that represents this situation.

• Use x to represent the number of one-person tubes rented and y to represent the number of cooler tubes rented.

• A one person tube costs $20 and a cooler tube costs $12.50

To find :

• The number of one-person tubes and cooler tubes rented

• System of linear equations

Solution :

Step 1 of 2 :

Find the System of linear equations

Let number of one-person tubes rented = x and number of cooler tubes rented = y

Since total 15 tubes were rented

∴ x + y = 15 - - - - - - - - (1)

Again one person tube costs $20 and a cooler tube costs $12.50

∴ Total cost = 20x + 12.50y

Since the group spends $270 to rent a total of 15 tubes

∴ 20x + 12.50y = 270 - - - - - - - - (2)

Hence system of linear equations are

x + y = 15 , 20x + 12.50y = 270

Step 2 of 2 :

Calculate number of one-person tubes and cooler tubes rented

x + y = 15 - - - - - - - - (1)

20x + 12.50y = 270 - - - - - - - - (2)

From Equation 1 and Equation 2 we get

20(15 - y) + 12.50y = 270

⇒ 300 - 20y + 12.50y = 270

⇒ 300 - 7.50y = 270

⇒ 7.50y = 300 - 270

⇒ 7.50y = 30

⇒ y = 30/7.50

⇒ y = 4

From Equation 1 we get

x + y = 15

⇒ x + 4 = 15

⇒ x = 15 - 4

⇒ x = 11

The number of one-person tubes rented = 11

The number of cooler tubes rented = 4

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