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

Answer:

The amount she started with $20

Step-by-step 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 = $(\frac{x- 10}{2} )$

amount left after this = $(\frac{x- 10}{2} )$

she further spent $4 on cofee, the remaining money = $(\frac{x- 10}{2} )$ - 4

she also spent 1/4 of remaining money on souveniers = $\frac{1}{4}(\frac{x-10}{2} - 4)$

amount left = $\frac{3}{4}(\frac{x-10}{2} - 4)$

The two last fractions should sum up to 1;

$\frac{1}{4}(\frac{x-10}{2} - 4) + \frac{3}{4}(\frac{x-10}{2} - 4) = 1\\\\\frac{x-10}{8} -1 + \frac{3x-30}{8} -3= 1\\\\\frac{x-10}{8} + \frac{3x-30}{8} = 1+3+1\\\\\frac{x-10}{8} + \frac{3x-30}{8} = 5\\\\\frac{x-10 +3x-30}{8} = 5\\\\\frac{4x-40}{8} =5\\\\4x-40 =40\\\\4x =80\\\\x = 20$

x = $20

Therefore, the amount she started with $20