At an agricultural cooperative, 0.45 of the total fruit harvested by weight consisted of a… — GMAT

At an agricultural cooperative, $0.45$ of the total fruit harvested by weight consisted of apples, and $\frac{3}{8}$ of the remaining fruit weight consisted of pears. If the remaining $550$ kilograms of fruit consisted entirely of oranges, what was the total weight, in kilograms, of the fruit harvested?

Answer: 1600 kg

Answer

1600

Subtracting the apple portion leaves 55% (or 11/20) of the total harvest. Since pears make up 3/8 of this remainder, oranges make up the remaining 5/8 of the 11/20 portion, which simplifies to 11/32 of the total harvest. Setting 11/32 of the total harvest equal to 550 kg yields a total weight of 1,600 kg.

Step-by-Step Solution

Find the fraction of the total harvest left after subtracting the apples.

The remaining portion is 1 - 0.45 = 0.55, which equals 11/20 of the total harvest.

Apples account for 0.45 of the harvest.

Calculate the portion of the harvest represented by oranges.

Since pears are 3/8 of the remainder, oranges are 5/8 of the remainder. Thus, oranges are (5/8) * (11/20) = 11/32 of the total harvest.

The non-apple harvest consists only of pears and oranges.

Solve for the total weight using the given weight of oranges.

Total weight = 550 * (32 / 11) = 1600 kg.

11/32 of the total weight equals 550 kilograms.

Key Concept

Multi-step arithmetic combining decimals and fractions to solve remaining-quantity word problems

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