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Part-to-Whole Ratios: Public Worked Question

A public ratio question that shows how to convert a part-to-part ratio into a part-to-whole share before scaling to a real quantity.

Question

A greenhouse prepares plant food by mixing concentrate and water in a ratio of 2:52:5. How many liters of concentrate are needed to prepare 3535 liters of the finished mixture?

  1. a.77 liters
  2. b.1010 liters
  3. c.1414 liters
  4. d.2525 liters

Correct answer

B. 1010 liters

Full reasoning

  1. 1The ratio 2:52:5 means the mixture consists of 2+5=72 + 5 = 7 equal parts.
  2. 2One part is 35÷7=535 \div 7 = 5 liters.
  3. 3The concentrate accounts for 22 parts, so it takes 2×5=102 \times 5 = 10 liters, and the water accounts for the remaining 2525 liters.

Why each choice is right or wrong

Choice A

This divides the total volume by the water part alone, 35÷535 \div 5, instead of dividing by the full 2+5=72 + 5 = 7 parts and then multiplying by the concentrate's share.

Choice B

Correct. The mixture has 2+5=72 + 5 = 7 equal parts, each part is 35÷7=535 \div 7 = 5 liters, and the concentrate fills 2×5=102 \times 5 = 10 liters.

Choice C

This treats the part-to-part ratio 2:52:5 as a part-to-whole fraction and computes 25×35\tfrac{2}{5} \times 35, ignoring that 55 is the water share, not the whole.

Choice D

This is the volume of water in the mixture, 5×5=255 \times 5 = 25 liters, so it answers the wrong part of the ratio.

Related formula

Part-to-whole share from a ratio

quantity=parta+b×total\text{quantity} = \frac{\text{part}}{a + b} \times \text{total}

Assumptions: The two ratio parts together account for the entire mixture with nothing left over.

Related topic and practice

Ratios, Rates, and ProportionsSign in for current practice

This public explainer is separate from the protected practice bank. Current practice coverage varies.

Source and public-release record

Authored for this public explainer registry. It has no database question ID and is not copied from a protected or official exam bank.

  1. Prealgebra 2e, Section 5.6: Ratios and Rate — OpenStax. Accessed 2026-07-11. OpenStax textbook content is CC BY 4.0; attribute and avoid verbatim reuse beyond short cited references.

Review and maintenance

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Keiko Study editorial owner
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Technical reviewer pending
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Last source check
2026-08-07
Next scheduled review
2026-11-07

Recheck the cited OpenStax reference before each major preparation cycle.

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