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A beverage company prepared two batches of sports drink, Batch A and Batch B, by mixing electrolyte concentrate with water. Batch A contained 25% electrolyte concentrate by volume, and Batch B contained 40% electrolyte concentrate by volume. What was the volume of Batch A?
(1) The total volume of electrolyte concentrate in the two batches was 34 liters.
(2) The total volume of the two batches was 100 liters.
(1) The total volume of electrolyte concentrate in the two batches was 34 liters.
(2) The total volume of the two batches was 100 liters.
05 Aug 2026, 23:00
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Official Solution:
A beverage company prepared two batches of sports drink, Batch A and Batch B, by mixing electrolyte concentrate with water. Batch A contained 25% electrolyte concentrate by volume, and Batch B contained 40% electrolyte concentrate by volume. What was the volume of Batch A?
Let \(A\) be the volume of Batch A, and let \(B\) be the volume of Batch B. The question asks for \(A\).
Since Batch A was \(25\%\) concentrate and Batch B was \(40\%\) concentrate, the total amount of concentrate was:
\(0.25A + 0.40B\)
(1) The total volume of electrolyte concentrate in the two batches was 34 liters.
So:
\(0.25A + 0.40B = 34\)
This is one equation with two unknowns, so \(A\) cannot be determined.
Not sufficient.
(2) The total volume of the two batches was 100 liters.
So:
\(A + B = 100\)
This is one equation with two unknowns, so \(A\) cannot be determined.
Not sufficient.
(1)+(2) We have two distinct linear equations with two unknowns, \(0.25A + 0.40B = 34\) and \(A + B = 100\), so we can solve for both. Sufficient.
Answer: C
A beverage company prepared two batches of sports drink, Batch A and Batch B, by mixing electrolyte concentrate with water. Batch A contained 25% electrolyte concentrate by volume, and Batch B contained 40% electrolyte concentrate by volume. What was the volume of Batch A?
Let \(A\) be the volume of Batch A, and let \(B\) be the volume of Batch B. The question asks for \(A\).
Since Batch A was \(25\%\) concentrate and Batch B was \(40\%\) concentrate, the total amount of concentrate was:
\(0.25A + 0.40B\)
(1) The total volume of electrolyte concentrate in the two batches was 34 liters.
So:
\(0.25A + 0.40B = 34\)
This is one equation with two unknowns, so \(A\) cannot be determined.
Not sufficient.
(2) The total volume of the two batches was 100 liters.
So:
\(A + B = 100\)
This is one equation with two unknowns, so \(A\) cannot be determined.
Not sufficient.
(1)+(2) We have two distinct linear equations with two unknowns, \(0.25A + 0.40B = 34\) and \(A + B = 100\), so we can solve for both. Sufficient.
Answer: C
