Problem Statement
Dr. Johnson spends one-fifth of the money in his wallet. Following this, he spends one-fifth of the remaining amount. 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.
Step-by-Step Breakdown
1. The first expenditure is one-fifth of M:
– Amount spent: 1/5 M
2. After this initial spending, the remaining amount in the wallet is:
– Remaining amount: M – 1/5 M = 4/5 M
3. Next, Dr. Johnson spends one-fifth of the remaining amount:
– Amount spent: 1/5 (4/5 M) = 4/25 M
4. The total amount spent is given as $36.00:
– Equation: 1/5 M + 4/25 M = 36
Combining Terms
To simplify the equation, we rewrite the first term:
– 1/5 M can be expressed as 5/25 M.
Now, the equation becomes:
– 5/25 M + 4/25 M = 36
Combining the fractions yields:
– 9/25 M = 36
Solving for M
To eliminate the fraction, multiply both sides by 25:
– 9M = 36 × 25
Calculating the right side gives:
– 9M = 900
Finally, divide both sides by 9 to find M:
– M = 100
Conclusion
Dr. Johnson initially had $100 in his wallet.