Question

Ali had 3 times as many marbles as cho does. After cho gives 4 marbles to Ali, Ali has 18 more marbles than cho does. How many more marbles does cho have in the beginning
a. 5
b. 9
c. 10
d. 15

Answer 1

Answer:

d. 15

Step-by-step explanation:

Let A and C be the initial number of marbles Ali and Cho have, respectively.

We are told that:

A = 3C  [Ali had 3 times as many marbles as cho does]

We then discover that  

C-4 = A-18   [After cho gives 4 marbles to Ali, Ali has 18 more marbles than cho does]

How many more marbles does cho have in the beginning?

We have 2 equations and 2 unknowns (A and C).  That means we can likely rearrange one of the equations and isolate one unknown on the left, and then use that in the second equation.

The first equation already has one of the unknowns isolated (A) so I'll use that in equation 2.

Eq. 1:   A = 3C

Eq. 2:  C-4 = A-18

Use the definition of A from Eq. 1 (=3C) to replace A in Eq. 2:

Eq. 2:  C-4 = A-18

          C-4 = (3C)-18    [Replace A with 3C, as promised in E1q. 1]

        -2C = -14

            C=7

If C = 7, then from Eq. 1,  A = 21

In the beginning, Ali has 21 marbles and Cho has 7.

Cho has 15 more marbles than Ali in the beginning.

a. 5

b. 9

c. 10

d. 15