Can you help with this question please?

Question

This is on the practice exam:

 

Diane, Rafael, and Hong have a total of $100 in their wallets. Hong has 2 times what Rafael has. Rafael has $8 less than Diane. How much do they have in their wallets? 

Answer 1

Let the amount Diane has = D

Let the amount Rafael has = D - 8

Let the amount Hong has = 2(D - 8) = 2D - 16

 

Using these variables, we can set up an equation that represents the total.

 

D + D - 8 + 2D - 16 = 100

 

 

Solve the equation for D.  Once you have the value of D, substitute that value into the variables to get each person's amount.

Answer 2

Notice in the words of the problem Diane is the last person mentioned.

 

Let Diane = d

 

then Rafael = d - 8

 

and Hong = 2(d - 8)

 

The sum of these 3 people is $100.  Write the equation.

 

d + d - 8 + 2(d - 8) = $100                  Distribute

 

d + d - 8 + 2d - 16 = $100                   Combine like terms

 

                  4d - 24 = $100                  Add 24 to both sides

 

                         4d = $124                  Divide both sides by 4

 

                           d = $31   This is the amount of money Diane has

 

Rafael = d - 8 = $31 - $8 = $23   This is the amount of money Rafael has

 

Hong has twice Rafael = 2($23) = $46  This is the amount of money Hong has

 

CHECK

 

The sum of the money is $100

 

$31 + $23 + $46 = $100   √