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Zorluk: KolayDirect Proportions

A commercial bakery makes a standard pastry dough using a ratio of 77 parts flour to 33 parts butter by weight. If a daily batch requires 4242 pounds of flour, how many pounds of butter are needed?

  1. 1818Cevap
  2. B
    6060
  3. C
    9898
  4. D
    126126

Cevap

1818
The ratio of flour to butter is given as 7:37:3. Setting up a direct proportion where xx is the pounds of butter needed: 73=42x\frac{7}{3} = \frac{42}{x}. Cross-multiplying gives 7x=1267x = 126. Solving for xx yields x=18x = 18 pounds of butter.

Adım Adım Çözüm

1
Identify the given ratio and the known quantity.
The ratio of flour to butter is 7:37:3. The known quantity of flour is 4242 pounds.
To set up a proportion, we must align the correct parts of the ratio with the real-world amounts.
2
Set up a direct proportion equation.
73=42x\frac{7}{3} = \frac{42}{x}
The ratio of parts must equal the ratio of the actual weights.
3
Solve for the unknown value xx.
7x=3×42→7x=126→x=187x = 3 \times 42 \rightarrow 7x = 126 \rightarrow x = 18
Cross-multiplying and dividing isolates the variable to find the required pounds of butter.

Anahtar Kavram

Direct Proportions
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Direct Proportions

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