Finding the initial number

Algebra
Tutor: None Selected Time limit: 1 Day

Carli spent two-thirds of her money and then spent $4 more.  Then she spent half of her remaining money.  It cost her $1 for the bus ride home.  She then had $5 left over.  How much money did she start with?

May 14th, 2015

Go from back to front:

She had $5 left, add her $1 from the bus journey: $6.

If she spent half of her remaining money, that means what she had before, the value x, satisfies:

(1/2) * x = $6

Multiplying each side by 2 gives: x = $12.

Then add the $4 more she spent: $16.

Then the money she started with, the value y, satisfies: 

(1/3) * y = $16: (she spent two thirds of her money so she only has a third of the original value left)

Multiplying each side by 3 gives: y = 16 * 3 = $48.

Therefore, Carli started with $48.

May 14th, 2015

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