Question

Brandi puts $15 of her paycheck into a savings account. She then spends half of what is left on clothes. She pays $24 for a concert ticket and later spends one-half of what is left on a book. When Brandi arrives back home, she has$14 left. What was the amount of Brandi's paycheck?

Answer 1

Brandy started with $119.

Explanation:

Let Brandy has the total amount = $x

She puts $15 of her paycheck into a saving account.

Amount left with her = $(x - 15)

She then spends half of what is left on clothes so the amount left =
`((x-15))/(2)`

Now she pays $24 for a concert ticket then money left with her =
`((x-15))/(2)` - 24

Later she spends one half of what she has on a book then the amount she has =
`(1)/(2)[((x-15))/(2)-24]`

When Brandy returns her home, she had $14 left with.

Therefore, the equation showing the amount left with Brandy will be

`(1)/(2)[((x-15))/(2)-24]` = 14

`((x-15))/(2)` - 24 = 14×2

`((x-15))/(2)-24=28`

`((x-15))/(2)=28+24`

`((x-15))/(2)=52`

x - 15 = 52×2

x - 15 = 104

x = 104 + 15

x = $119

Therefore, Brandy started with $119.

Answer 2

Explanation:

Start backwards.

She has 14 dollars when she gets home.

That is 1/2 of what she had left after buying the book. The book must have cost 14 dollars.

Before buying the book she must have had 14 + 14 = 28 dollars.

She bought a concert ticket for 24 dollars which adds to the 28. 24 + 28 = 52.

So at this point before buying the concert ticket, she has 52 dollars.

The 52 dollars represents 1/2 of what she had left before she put the 15 dollars in the savings account

52 + 52 is what she had before she bought clothing. = 104 dollars.

So the very first thing she did was put 15 dollars in her savings account

104 + 15 = 119 which was the amount of her check. Work forwards to see if it is right.

========================

She starts out with 119 dollars.

Savings = 15. Remainder = 104

Clothes = 52 Remainder = 52

Concert = 52 - 24 = 28

Book = 1/2 * (28) = 14

Remainder = 14 which is what she had when she got home.

Everything checks.