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

Answer:

13x + 10

Step-by-step 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.