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?
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