Question

1. The hot-water tank in Rafael's house holds 17x + 11 gallons of hot water. Rafael used 4x + 1 gallons of hot water washing the dishes. Which of the following

binomials represents the number of gallons of hot water remaining in the tank?

Answer 1

13x + 10

Explanation:

Rafael's hot-water tank holds:

`17x + 11`

Gallons of hot water.

Rafael used:

`4x + 1`

Gallons of hot water.

And we want to determine which binomial represent the amount of hot water remaining in the tank.

The amount remaining R in the tank will be the amount taken by Rafael subtracted from the total amount. Hence:

`\displaystyle R = (17x+11) - (4x + 1)`

Simplify. Distribute:

`\displaystyle R = (17x + 11) + (-4x - 1)`

Rearrange:

`R = (17x - 4x) + (11 - 1)`

Combine like terms:

`R = 13x + 10`

In conclusion, 13x + 10 gallons remain in the tank.