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?
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.
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