Problem Statement
Dr. Johnson spends one-fifth of the money in his wallet. He then spends one-fifth of what remains. In total, he spends $36.00. The question is: how much money did Dr. Johnson have initially?
Solution
Let M represent the initial amount of money in Dr. Johnson’s wallet. The spending can be broken down as follows:
First Spending
Dr. Johnson first spends one-fifth of his initial amount:
Amount spent: 1/5M
Remaining Amount After First Spending
After the first spending, the amount left in the wallet is:
Remaining Amount: M - 1/5M = 4/5M
Second Spending
Next, he spends one-fifth of the remaining amount:
Amount spent: 1/5(4/5M) = 4/25M
Total Spending Equation
The total amount spent by Dr. Johnson is the sum of both expenditures:
1/5M + 4/25M = 36
Finding a Common Denominator
To solve the equation, we find a common denominator:
1/5M + 4/25M = 36 becomes 5/25M + 4/25M = 36
Simplifying the Equation
This simplifies to:
9/25M = 36
Multiplying to Eliminate the Fraction
Next, we multiply both sides by 25 to eliminate the fraction:
9M = 36 × 25
Calculating M
Solving the equation gives:
9M = 900
M = 100
Conclusion
Dr. Johnson initially had $100 in his wallet.