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 = [tex](\frac{x- 10}{2} )[/tex]
amount left after this = [tex](\frac{x- 10}{2} )[/tex]
she further spent $4 on cofee, the remaining money = [tex](\frac{x- 10}{2} )[/tex] - 4
she also spent 1/4 of remaining money on souveniers = [tex]\frac{1}{4}(\frac{x-10}{2} - 4)[/tex]
amount left = [tex]\frac{3}{4}(\frac{x-10}{2} - 4)[/tex]
The two last fractions should sum up to 1;
[tex]\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[/tex]
x = $20
Therefore, the amount she started with $20
