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Zorluk: OrtaBasic Ratios

A civil engineering unit is mixing concrete for a rapid runway repair. The specialized mixture requires a weight ratio of 33 parts Portland cement to 55 parts aggregate. If a repair job requires a total of 400400 pounds of this dry mixture, how many pounds of Portland cement are needed?

  1. A
    5050
  2. 150150Cevap
  3. C
    240240
  4. D
    250250

Cevap

The correct amount is 150150 pounds.
The mixture consists of 33 parts cement and 55 parts aggregate, meaning there are 88 parts in total. Since the entire mixture weighs 400400 pounds, each part weighs 5050 pounds (400÷8400 \div 8). To find the amount of Portland cement, which represents 33 of those parts, we multiply 5050 by 33 to get 150150 pounds.

Adım Adım Çözüm

1
Determine the total number of parts in the given ratio.
3 (cement)+5 (aggregate)=8 total parts3 \text{ (cement)} + 5 \text{ (aggregate)} = 8 \text{ total parts}
Because the 400400 pounds represents the entire mixture, we need to know the total parts that make up that whole mixture.
2
Calculate the weight of one single part.
400÷8=50 pounds per part400 \div 8 = 50 \text{ pounds per part}
Dividing the total weight by the total number of parts gives the value of a single proportional unit.
3
Calculate the total weight of the Portland cement.
50×3=150 pounds50 \times 3 = 150 \text{ pounds}
The ratio specifies 33 parts of Portland cement, so we multiply the weight of one part by 33.

Anahtar Kavram

Solving part-to-whole ratio problems by finding the sum of the ratio parts and determining the unit value of a single part.
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Basic Ratios

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