At an agricultural orchard, a seasonal harvest consisted of apples, pears, and peaches. Of… — ACT

At an agricultural orchard, a seasonal harvest consisted of apples, pears, and peaches. Of the total harvest, $\frac{3}{8}$ were apples and $42.5\%$ were pears. If the remaining harvest consisted of $96$ bushels of peaches, what was the total number of bushels of fruit harvested by the orchard?

A
$120$
B
$256$
C
$384$
$480$ Cevap
E
$640$

Cevap

The total harvest was 480 bushels of fruit.

Converting the fraction of apples

\frac{3}{8}

gives

37.5\%

. Combining this with the

42.5\%

of pears yields

80\%

of the total harvest. The remaining

20\%

of the harvest represents the

96

bushels of peaches. Dividing

96

0.20

gives the total harvest of

480

bushels.

Adım Adım Çözüm

Convert the fraction of apples to a percentage.

\frac{3}{8} = 0.375 = 37.5\%

Converting all quantities to percentages allows for direct addition and comparison.

Find the combined percentage of apples and pears.

37.5\% + 42.5\% = 80\%

Adding the percentage of apples and pears determines the portion of the harvest that is not peaches.

Calculate the percentage representing peaches.

100\% - 80\% = 20\%

The remaining percentage of the total harvest corresponds to the peaches.

Solve for the total number of bushels harvested.

96 \div 0.20 = 480

bushels

Dividing the number of peach bushels by its corresponding decimal fraction (

0.20

) yields the total harvest.

Anahtar Kavram

Solving word problems involving mixed fractions, decimals, percentages, and unknown total quantities.

Tahmini Süre:1m 15s

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