A natural foods supplier is mixing up a rice blend that contains 25% wild rice. They already have 1 pound of a blend that contains 29% wild rice. To this, they will be adding a second blend that contains 24% wild rice. How much of the second blend should be added to obtain the desired 25% wild rice blend?

Question

Write your answer as a whole number or as a decimal rounded to the nearest tenth.
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Answer 1

To solve the problem, we can set up an equation based on the amount of wild rice in each mixture.

Let's denote the amount of the second blend to be added as \( x \) pounds.

1. The first blend weighs 1 pound and contains 29% wild rice: \[ \text{Wild rice from blend 1} = 0.29 \times 1 = 0.29 \text{ pounds} \]

2. The second blend contains 24% wild rice, so from \( x \) pounds of the second blend, the amount of wild rice will be: \[ \text{Wild rice from blend 2} = 0.24 \times x \text{ pounds} \]

3. The total amount of the blend after adding \( x \) pounds will be: \[ 1 + x \text{ pounds} \]

4. The total amount of wild rice in the new blend will thus be: \[ \text{Total wild rice} = 0.29 + 0.24x \text{ pounds} \]

5. We want the resulting mixture to contain 25% wild rice. Therefore, we can set up the equation: \[ \frac{0.29 + 0.24x}{1 + x} = 0.25 \]

6. To eliminate the fraction, we multiply both sides by \( 1 + x \): \[ 0.29 + 0.24x = 0.25(1 + x) \]

7. Expanding the right-hand side: \[ 0.29 + 0.24x = 0.25 + 0.25x \]

8. Rearranging the equation: \[ 0.29 - 0.25 = 0.25x - 0.24x \] \[ 0.04 = 0.01x \]

9. Solving for \( x \): \[ x = \frac{0.04}{0.01} = 4 \]

Therefore, the amount of the second blend that should be added to obtain the desired 25% wild rice blend is \( \boxed{4} \) pounds.