How much money did each boy have to begin with?

Question

Darius and Daniel each had an equal amount of money to spend. After Darius spent 360.00 and Daniel spent 150.00. Daniel had 8 times as much money as what Darius had left. How much money did each boy have to begin with

Answer 1

a = b

a - 150 = 8(b - 360)

a - 150 = 8b - 2880

a = 8b - 2730

 

Since a = b and a = 8b - 2730, then...

 

b = 8b - 2730

7b = 2730

b = 390

 

Aaaaaand, since a = b, a = 390

 

Each started with $390.

Answer 2

Since Darius and Daniel each had an equal amount of money to spend (and because this is the amount we are wanting to find) we can let "d" denote the variable for this amount. Now it is given to us that Darius spent $360 and Daniel spent $150. So, we can let "d - 360" denote the amount of money Darius has left, and we can let "d - 150" denote the amount of money Daniel has left. Finally, we are given that the amount of money Daniel has left (d - 150) is equal to 8 times the amount of money Darius had left (d - 360). Therefore,

 

d - 150 = 8(d - 360)

d - 150 = 8d - 2880

-150 = 7d - 2880

7d = 2730

d = 390

 

So, the amount of money each boy had to begin with is $390.00.