Multi step equation

Question

Dennis bought a variety pack of delicious donuts from Dunkin Donuts from his girlfriend Liz's store for his friends Bubba and Hooch. Bubba ate two-thirds of the pack and Hooch devoured one-fourth of them. Finally Dennis, starving as he was, ate the remaining one donut (He probably should have bought more). What was the total number of donuts Dennis bought?

Answer 1

12 is correct. Dennis bought a dozen donuts.

Answer 2

Hello, Jeff,

Assign the letters D, B, and H to the three donut men. Let T be the total donuts. Then set equations to what we know:

D = 1 (Dennis has one donut)

B = (2/3)T (Bubba gets 2/3 of the donuts)

H = (1/4)T (Hubba gets 1/4)

The total, T must equal the sum of these three:

T = (2/3)T + (1/4)T + 1

T = (8/12)T + (3/12)T + 1

T = (11/12)T + 1

(1/12)T = 1

Ta da . . .

T = 12

Check to see if 12 donuts works. (2/3) * 12 + (1/4) * 12 +1 =? = 8 + 3 + 1 = 12 Yes

I hope this helps,

Bob