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Zorluk: OrtaFractions, Decimals, and Percentages

An artisanal bakery prepares a specialty flour blend consisting of rye, oat, and wheat flour. By weight, 310\frac{3}{10} of the blend is rye flour and 0.450.45 of the blend is oat flour. The remaining portion of the blend is wheat flour. If a single batch of the blend contains 4.54.5 pounds of wheat flour, what is the total weight, in pounds, of the flour blend prepared for the batch?

Cevap: 18 pounds

Cevap

The total weight of the flour blend prepared for the batch is 18 pounds.
To find the total weight of the mixture, first determine the decimal fraction representing wheat flour. Converting 310\frac{3}{10} to 0.300.30, the combined proportion of rye and oat flour is 0.30+0.45=0.750.30 + 0.45 = 0.75. Wheat flour makes up the remaining 1−0.75=0.251 - 0.75 = 0.25 (25%25\%) of the mixture. Setting up the equation 0.25×Total Weight=4.50.25 \times \text{Total Weight} = 4.5 gives Total Weight=4.50.25=18\text{Total Weight} = \frac{4.5}{0.25} = 18 pounds.

Adım Adım Çözüm

1
Convert the fraction of rye flour to a decimal and sum it with the oat flour portion.
Rye portion = 310=0.30\frac{3}{10} = 0.30; Combined Rye and Oat portion = 0.30+0.45=0.750.30 + 0.45 = 0.75.
Converting all given values to a consistent decimal format allows for straightforward addition.
2
Calculate the remaining portion representing wheat flour.
Wheat portion = 1−0.75=0.251 - 0.75 = 0.25.
The sum of all proportional components in a whole mixture equals 1.
3
Divide the weight of the wheat flour by its decimal proportion to solve for the total batch weight.
Total weight = 4.50.25=18\frac{4.5}{0.25} = 18 pounds.
Since 25%25\% (0.250.25) of the total weight is 4.54.5 pounds, dividing the part by its decimal rate yields the total whole.

Anahtar Kavram

Solving multi-step word problems involving conversions between fractions, decimals, and percentages to find an unknown total.
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Fractions, Decimals, and Percentages

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