Peter had some money. He spent 2/5 of his money on a bag and 1/3 of the reminder on a shirt. he spent $35 more on the bag than the shirt. How much money did Peter have left?

Answer 1

m = Peter"s money

He spent 2 / 5 m of his money on a bag.

Reminder = m - 2 / 5 m =

5 / 5 m - 2 / 5 m = 3 / 5 m

He spent 1 / 3 of the reminder on a shirt, so he spent:

1 / 3 ( 3 / 5 m ) = 1 / 3 • 3 / 5 m =

1 / 5 m on a shirt.

Total he spent 2 / 5 m + 1 / 5 m =

3 / 5 m

He have left m - 3 / 5 m =

5 / 5 m - 3 / 5 m = 2 / 5 m

He spent $35 more on the bag than the shirt means:

2 / 5 m = 1 / 5 m + 35

Subtract 1 / 5 m to both sides

1 / 5 m = 35

m = 5 • $35 = $175

He have left 2 / 5 m = 2 / 5 • 175 =

2 • 175 / 5 = $70

Check result:

He spent 2 / 5 m of his money on a bag.

He spent 2 / 5 • $ 175 =

2 • $175 / 5 = $70 on a bag.

The reminder = $175 - $70 = $105

He spent 1 / 3 of the reminder on a shirt.

He spent 1 / 3 • $105 =

$105 / 3 = $35 on a shirt.

He spent $35 more on the bag than the shirt.

$70 - $35 = $35