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Zorluk: OrtaWeighted Average and Combined Sets

A commercial bakery produces two batches of bread dough. Batch X consists of 3030 kilograms of dough with a sugar concentration of 12%12\% by weight. Batch Y consists of 4545 kilograms of dough with a sugar concentration of 20%20\% by weight. If Batch X and Batch Y are mixed together completely, what is the sugar concentration, as a percentage by weight, of the combined mixture?

Cevap: 16.8 %

Cevap

The sugar concentration of the combined mixture is 16.8 percent by weight.
The overall concentration is calculated by taking the weighted average of the two concentrations. Since Batch X and Batch Y have weights in the ratio of 2 to 3, the overall percentage is [2(12%) + 3(20%)] / (2 + 3) = 84 / 5 = 16.8%. Alternatively, the total amount of sugar is 3.6 kg + 9.0 kg = 12.6 kg out of a total mass of 75 kg, yielding 12.6 / 75 = 16.8%.

Adım Adım Çözüm

1
Calculate the total mass of sugar contributed by Batch X
3.6 kg of sugar (30×0.12=3.630 \times 0.12 = 3.6)
To find the total sugar in the combined mixture, compute the sugar content from each component batch.
2
Calculate the total mass of sugar contributed by Batch Y
9.0 kg of sugar (45×0.20=9.045 \times 0.20 = 9.0)
Compute the sugar mass for the second batch.
3
Sum the total sugar mass and total batch mass
Total sugar = 12.612.6 kg (3.6+9.03.6 + 9.0); Total mass = 7575 kg (30+4530 + 45)
The combined concentration equals total sugar divided by total mixture mass.
4
Compute the combined percentage concentration
16.8% (12.675×100%=16.8%\frac{12.6}{75} \times 100\% = 16.8\%)
Divide total sugar mass by total mixture mass and multiply by 100.

Anahtar Kavram

Weighted Average of Combined Sets
Tahmini Süre:1m 30s
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Weighted Average and Combined Sets

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