Celine planted a vegetable garden and plans to fertilize it. In the shed, her dad has two bags of fertilizer, one that contains 18% nitrogen and another that contains 4% nitrogen. After doing some research and testing the soil, Celine decides she needs 3.5 pounds of fertilizer that contains 12% nitrogen. How many pounds of each bag of fertilizer should Celine mix together?

Question

Write your answers as whole numbers, decimals, or simplified fractions or mixed numbers. Do not round.
pounds of the 18%-nitrogen fertilizer
pounds of the 4%-nitrogen fertilizer

Answer 1

Let \( x \) be the pounds of the 18% nitrogen fertilizer, and let \( y \) be the pounds of the 4% nitrogen fertilizer. We have two equations based on the information given:

1. The total weight of the fertilizer should be 3.5 pounds: \[ x + y = 3.5 \]

2. The total amount of nitrogen in the mixture should equal 12% of 3.5 pounds: \[ 0.18x + 0.04y = 0.12 \times 3.5 \]

Calculating \( 0.12 \times 3.5 \): \[ 0.12 \times 3.5 = 0.42 \] So the second equation becomes: \[ 0.18x + 0.04y = 0.42 \]

Now we have the system of equations:

1. \( x + y = 3.5 \)
2. \( 0.18x + 0.04y = 0.42 \)

We can solve this system using substitution or elimination. Let's use substitution by solving the first equation for \( y \):

\[ y = 3.5 - x \]

Now, substitute \( y \) into the second equation:

\[ 0.18x + 0.04(3.5 - x) = 0.42 \] Distributing the \( 0.04 \): \[ 0.18x + 0.14 - 0.04x = 0.42 \] Combining like terms: \[ (0.18 - 0.04)x + 0.14 = 0.42 \] \[ 0.14x + 0.14 = 0.42 \] Subtracting \( 0.14 \) from both sides: \[ 0.14x = 0.28 \] Dividing by \( 0.14 \): \[ x = \frac{0.28}{0.14} = 2 \]

Now, substituting \( x = 2 \) back into the equation \( y = 3.5 - x \): \[ y = 3.5 - 2 = 1.5 \]

Thus, the amounts of each type of fertilizer are:

• Pounds of the 18%-nitrogen fertilizer: \( \boxed{2} \)
• Pounds of the 4%-nitrogen fertilizer: \( \boxed{1.5} \)