Question

The table below shows the number of times the dishwasher was used in three different houses over three days.

Dishwasher Use

House A
House B
House C
Friday
1
2
2
Saturday
2
3
4
Sunday
2
2
3

On Friday, 17.5 total gallons of water were used. On Saturday, 31.5 total gallons were used. On Sunday, 24.75 total gallons were used. What is the difference between the water use per load of the dishwasher that uses the most water and the dishwasher that uses the least water?
0.5 gallon
0.75 gallon
3 gallons
4 gallons

Answer 1

Let a, b, c be the gallons per load for houses A, B, C. From the daily totals:

Friday: a + 2b + 2c = 17.5
Saturday: 2a + 3b + 4c = 31.5
Sunday: 2a + 2b + 3c = 24.75

Subtract Friday from Saturday: a + b + 2c = 14
Subtract Friday from Sunday: a + c = 7.25 → a = 7.25 − c

From a + b + 2c = 14 ⇒ (7.25 − c) + b + 2c = 14 ⇒ b + c = 6.75 ⇒ b = 6.75 − c

Plug into Friday: (7.25 − c) + 2(6.75 − c) + 2c = 17.5 ⇒ 20.75 − c = 17.5 ⇒ c = 3.25
Then a = 4.0, b = 3.5.

Difference between max and min = 4.0 − 3.25 = 0.75 gallon.

Answer: 0.75 gallon.