Question

3. There are two candy machines in a restaurant. One is filled with 200 gumballs and the other

is filled with 900 chocolate candies. The gumballs are dispensed 1 at a time and the chocolate
candies are dispensed 8 candies at a time. How many dispenses from each machine will make
the number of candies in the machines equal?

Answer 1

100 dispenses

Explanation:

To check the answer:

Gumballs: 200 - (1*100) = 100

Explanation: 200 gumballs - (1 gumball * 100 dispenses) = 100 gumballs left.

Chocolate Candies: 900 - (8*100) = 100

Explanation: 900 candies - (8 candies * 100 dispenses) = 100 candies left.

Answer 2

100

Explanation:

Given a candy machine with 200 gumballs dispensed 1 at a time, and another with 900 chocolates dispensed 8 at a time, you want to know how many dispenses from each will result in equal counts left in the machines.

Gumballs

The number of remaining gumballs after d dispenses is ...

g = 200 -d

Chocolates

The number of remaining chocolates after d dispenses is ...

c = 900 -8d

Equal numbers

The number remaining in each machine will be equal when ...

g = c

200 -d = 900 -8d . . . . . substitute the above expressions

7d = 700 . . . . . . . . . . add 8d -200

d = 100 . . . . . . . . . divide by 7

100 dispenses from each machine will make the number of candies in the machines equal.