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Difficulty: EasyRatio, Proportion, and Rate

Three farmers, Audu, Ngozi, and Tayo, shared a bag of fertilizer in the ratio 2:3:52 : 3 : 5. If Ngozi received 45 kg45\text{ kg}, what was the total mass of the fertilizer shared?

  1. A
    75 kg75\text{ kg}
  2. B
    135 kg135\text{ kg}
  3. 150 kg150\text{ kg}Answer
  4. D
    225 kg225\text{ kg}

Answer

The total mass of the fertilizer shared was 150 kg150\text{ kg}.
The ratio 2:3:52 : 3 : 5 indicates that the fertilizer is divided into 2+3+5=102 + 3 + 5 = 10 equal parts. Ngozi receives 3 of these parts, which equals 45 kg45\text{ kg}. Dividing 45 kg45\text{ kg} by 3 gives 15 kg15\text{ kg} per part. Multiplying 15 kg15\text{ kg} by the total of 10 parts gives 150 kg150\text{ kg}.

Step-by-Step Solution

1
Find the total number of parts in the ratio.
Total parts = 2+3+5=102 + 3 + 5 = 10 parts.
The total quantity is divided into parts according to the given ratio 2:3:52 : 3 : 5.
2
Determine the value of 1 part using Ngozi's share.
Value of 1 part = 45 kg3=15 kg\frac{45\text{ kg}}{3} = 15\text{ kg}.
Ngozi corresponds to the middle term of the ratio, which is 3 parts out of 10.
3
Calculate the total mass by multiplying the value of 1 part by the total number of parts.
Total mass = 10×15 kg=150 kg10 \times 15\text{ kg} = 150\text{ kg}.
The total mass consists of all 10 parts combined.

Key Concept

Sharing quantities in a given ratio

Alternative Method

Use proportional fractions: Ngozi's fraction of the total is 310\frac{3}{10}. Let total mass be MM. Then 310M=45  ⟹  M=45×103=150 kg\frac{3}{10} M = 45 \implies M = 45 \times \frac{10}{3} = 150\text{ kg}.
Estimated Time:45s
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Topics

Ratio, Proportion, and Rate

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