Question

Two different juice concentrates, A and B, are used to form two different mixtures P and Q. To make P, xx ml of A and 40 ml of B are used; while to make Q, 90 ml of A and xx ml of B are used. It was observed that the juice concentration in each mixture, P and Q, is the same.

• A. Quantity A is greater.
• B. Quantity B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.

Hint:

When two mixtures have the same concentration, the ratio of amounts of each concentrate in each mixture should be equal.

Answer 1

The Correct Option is C

Let the amount of concentrate A in mixture P be \( x \) ml, and the amount of concentrate B be 40 ml. For mixture Q, 90 ml of concentrate A is used, and the amount of concentrate B is \( x \) ml. The concentrations in both mixtures are the same. Therefore, the ratio of concentrate A to concentrate B in each mixture must be equal. We can set up the following equation: For mixture P: \[ \frac{x}{40} \quad \text{(ratio of A to B in P)} \] For mixture Q: \[ \frac{90}{x} \quad \text{(ratio of A to B in Q)} \] Since the ratios are equal, we have: \[ \frac{x}{40} = \frac{90}{x} \] Multiplying both sides by \( x \times 40 \), we get: \[ x^2 = 3600 \] Solving for \( x \), we find: \[ x = 60 \] Thus, the value of \( x \) is 60 ml.
Final Answer: \[ \boxed{\text{The two quantities are equal.}} \]