Question

Ahmya bought $10 shirt. Spent 1/2 remaining money for dinner. Bought $4cofee, spent 1/4 of remaining money on souveniers. How much did she start with?

Answer 1

The amount she started with $20

Explanation:

Let the amount Ahmya started with = x

when she bought $10 shirt, the remaining money is = x - 10

she spent half of this remaining money on dinner =
`((x- 10)/(2) )`

amount left after this =
`((x- 10)/(2) )`

she further spent $4 on cofee, the remaining money =
`((x- 10)/(2) )` - 4

she also spent 1/4 of remaining money on souveniers =
`(1)/(4)((x-10)/(2) - 4)`

amount left =
`(3)/(4)((x-10)/(2) - 4)`

The two last fractions should sum up to 1;

`(1)/(4)((x-10)/(2) - 4) + (3)/(4)((x-10)/(2) - 4) = 1\\\\(x-10)/(8) -1 + (3x-30)/(8) -3= 1\\\\(x-10)/(8) + (3x-30)/(8) = 1+3+1\\\\(x-10)/(8) + (3x-30)/(8) = 5\\\\(x-10 +3x-30)/(8) = 5\\\\(4x-40)/(8) =5\\\\4x-40 =40\\\\4x =80\\\\x = 20`

x = $20

Therefore, the amount she started with $20