6.RP Jim and Jesse's Money
Jim and Jesse each had the same amount of money. Jim spent \($58\) to fill the car up with gas for a road-trip. Jesse spent \($37\) buying snacks for the trip. Afterward, the ratio of Jim’s money to Jesse’s money is \(1:4\). How much money did each have at first?
Solutions
We know that Jesse has $21 more than Jim after they make their purchases, because Jim spent $21 more than Jesse. Since the ratio of money they have remaining is \(1:4\), we know this difference is 3 times what Jim has left.
\(3 \text{ units } = $58 - $37 = $21\)
\(1 \text{ unit } = $7\)
We should add what Jim has left to what he spent:
\($58 + $7 = $65\)
They each had \($65\) at first.
We know that Jim spent $21 more than Jesse, so Jim has $21 less than Jesse after they make their purchases. Since Jim has only \(\frac14\) as much money as Jesse has, the difference between the two amounts is \(\frac34\) of the amount of money Jesse has. So 21 is \(\frac34\) of the amount of money Jesse has. Therefore, \(\frac14\)of the amount of money Jesse has is one third of this, or 7. So Jesse has \(4 \cdot 7=28\); and since he spent 37, he originally had \(28 + 37=65\). So Jim and Jesse each originally had $65.