multi step equation

Question

David bought a variety pack of delicious donuts from the famous Donut house for his daughters, Amy and Anna. Amy ate two-third of the pack and Anna devoured one-fourth of them. Finally David ate the remaining one donut. Find out the total number of donuts in the pack. 

Answer 1

Hello Jeff,

here we have to form an equation step by step and solve it

so you have to read the problem above carefully...

Lets assume the no of donuts ( Donuts pack ) David bought be x ,

From above condition , Amy ate = 2/3 x ( two third of x )

now remaining portion is x- 2/3x

Anna ate 1/4*( x-2/3x) that is one fourth of the remaining part of Amy ate .

we can calculate this 1/4*( x- 2/3x) = 1/4x - 1/4*2/3x = 1/4x- 1/6x

David ate remaning 1, as per the condition above

Now adding all 3 people Donut portion , it will be equal the whole Donuts pack, we can write the equation,

x = 2/3x + 1/4x - 1/6x + 1

x = 11x/12 - 1/6x + 1 ( solving the equation step by step )

x = 9x/12 + 1 ( 9x/12 can be written as 3x/4 )

x = 3x/4 + 1

subtracting both sides 3x/4 we get,

x - 3x/4 = 1

x/4 = 1 ( as x - 3x/4 = x/4 )

multiplying both sides by 4 ,

x = 4

so there are total no of Donuts 4 ....Ans

we can recheck it by reverse calculation with your answer here .

Answer 2

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

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

(11/12)D + 1 = D

(12/12)D - (11/12)D = 1

(1/12)D = 1

D = 12 donuts in the pack

Amy ate 2/3 of 12 = 8 donuts

Anna ate 1/4 of 12 = 3 donuts

David ate the last = 1 donut

8+3+ 1 = 12