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Zorluk: OrtaRatios and Proportions

A naval shipyard allocates its weekly steel supply for submarine repair, surface ship repair, and new construction in a ratio of 3:4:53:4:5. If the surface ship repair division receives 240240 tons of steel, what is the total amount of steel allocated to all three divisions combined?

  1. A
    480
  2. B
    576
  3. 720Cevap
  4. D
    960

Cevap

The total amount of steel allocated to all three divisions is 720 tons.
The ratio of steel for submarine repair, surface ship repair, and new construction is 3:4:53:4:5, which means there are 1212 total parts (3+4+53+4+5). We are given that surface ship repair, the middle term representing 44 parts of the ratio, receives 240240 tons. To find the value of a single part, divide 240240 by 44, yielding 6060 tons. Finally, multiply this unit rate by the 1212 total parts to find the total steel allocation: 60×12=72060 \times 12 = 720 tons.

Adım Adım Çözüm

1
Identify the number of ratio parts assigned to surface ship repair and calculate the total number of parts.
Surface ship repair = 4 parts. Total parts = 3 + 4 + 5 = 12 parts.
To find the value of a single part, we must correctly match the given amount to its corresponding ratio value.
2
Calculate the amount of steel that corresponds to one ratio part.
240 tons / 4 parts = 60 tons per part.
Finding this unit rate allows us to scale up to the total amount.
3
Multiply the unit rate by the total number of parts.
60 tons/part * 12 parts = 720 tons.
The question asks for the total amount of steel allocated to all three divisions combined.

Anahtar Kavram

Solving multi-part ratio problems by finding a unit rate

Alternatif Yöntem

You can set up a direct proportion: 4 parts / 240 tons = 12 total parts / x tons. Cross-multiplying gives 4x = 2880, so dividing both sides by 4 yields x = 720.
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Konular

Ratios and Proportions

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