A fruit seller had the same number of papayas and mangoes at first. He
threw away 85 rotten papayas and sold 1/4 of his remaining papayas. He
threw away 60 rotten mangoes and sold 1/3 of his remaining mangoes. After
that, he was left with an equal number of papayas and mangoes.
(a) How many papayas did the fruit seller have at first?
(b) The fruit seller sold his mangoes at 3 for $5.80. How much did he
collect from the sale of the mangoes?
To solve this problem, we can use a logical approach and work backwards. Let's break it down step by step:
Step 1: Set up the equations:
Let's assume that the initial number of papayas and mangoes is "x".
Step 2: Account for rotten papayas:
After throwing away 85 rotten papayas, the number of remaining papayas is (x - 85).
Step 3: Account for papayas sold:
The fruit seller sold 1/4 of his remaining papayas, so the number of papayas sold is (1/4)(x - 85).
Step 4: Account for rotten mangoes:
After throwing away 60 rotten mangoes, the number of remaining mangoes is (x - 60).
Step 5: Account for mangoes sold:
The fruit seller sold 1/3 of his remaining mangoes, so the number of mangoes sold is (1/3)(x - 60).
Step 6: Set up the final equation:
According to the problem, the fruit seller was left with an equal number of papayas and mangoes. Therefore, we can set up the equation (x - 85 - (1/4)(x - 85)) = (x - 60 - (1/3)(x - 60)).
(a) How many papayas did the fruit seller have at first?
Solving the equation from step 6 will give us the value of "x," which represents the initial number of papayas and mangoes.
(b) The fruit seller sold his mangoes at 3 for $5.80. How much did he collect from the sale of the mangoes?
To find this, we need to determine the number of mangoes sold and then multiply it by the price of 3 mangoes.