Bruce had some money in his wallet. He spent $390 on a watch and \(\frac{5}{7}\) of the remaining money on a belt. The amount of money left in the wallet was \(\frac{1}{10}\) of the amount he had at first. How much money did he have at first?
Answer (1)
To find out how much money Bruce initially had, we can set up an equation based on the information provided in the question.
Let's say Bruce had x dollars initially.
Bruce spent $390 on a watch. Therefore, the remaining money after buying the watch is: x − 390
After buying the watch, Bruce spent 7 5 of the remaining money on a belt. So the amount spent on the belt is: 7 5 × ( x − 390 )
The remaining money after both purchases is thus: ( x − 390 ) − 7 5 ( x − 390 ) This simplifies to: 7 2 ( x − 390 )
According to the problem, the money left in the wallet is 10 1 of the original amount Bruce had. Therefore, we can set up the equation: 7 2 ( x − 390 ) = 10 1 x
Now, we solve this equation for x :
First, multiply both sides by 70 (the common denominator of 7 and 10) to clear the fractions: 20 ( x − 390 ) = 7 x
Distribute on the left side: 20 x − 7800 = 7 x
Subtract 7 x from both sides to get: 13 x − 7800 = 0
Add 7800 to both sides: 13 x = 7800
Divide by 13: x = 600
Therefore, Bruce initially had $600 in his wallet.
