Roy saves 20% of his daily pocket money. If his daily pocket money increases by 30%, his savings will increase by 60 cents. Find the amount of his daily pocket money before the increase.
Question
Roy saves 20% of his daily pocket money. If his daily pocket money increases by 30%, his savings will increase by 60 cents. Find the amount of his daily pocket money before the increase.
Solution
Step 1: Let's denote Roy's daily pocket money as P. According to the problem, Roy saves 20% of P, which is 0.2P.
Step 2: The problem states that if his daily pocket money increases by 30%, his savings will increase by 60 cents. This means that the new amount of money he saves is 0.2P + 60 cents.
Step 3: The new amount of money he saves is also 20% of his new daily pocket money, which is 1.3P (since his pocket money increased by 30%). So, we can set up the equation 0.2P + 60 cents = 0.2 * 1.3P.
Step 4: Simplify the equation to 0.2P + 60 = 0.26P.
Step 5: Rearrange the equation to find P. Subtract 0.2P from both sides to get 60 = 0.06P.
Step 6: Divide both sides by 0.06 to find P. P = 60 / 0.06 = 1000 cents.
Step 7: Convert cents to dollars (since pocket money is usually given in dollars). P = 1000 cents = $10.
So, Roy's daily pocket money before the increase was $10.
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