I'm not sure of how to solve word problems. The question is,"One lawn fertilizer is 24% nitrogen and another is 12% nitrogen. How much of fertilizer should be mixed to obtain 100 kg of fertilizer that is 21% nitrogen?"
Nitrogen total=sum of parts
100*.21=.24*x + .12y
but x+y=100
21=.24x+.12(100-x)
solve for x first.
To solve this word problem, we need to set up an equation using the concept of weighted averages. Here's how to do it step by step:
Step 1: Identify the given information:
- First fertilizer: 24% nitrogen
- Second fertilizer: 12% nitrogen
- Target fertilizer mixture: 21% nitrogen
- Total weight of the mixture: 100 kg
Step 2: Assign variables:
Let's assign variables for the weights of the first and second fertilizers. You can use any variables you'd like, but for simplicity, let's use "x" for the weight of the first fertilizer (24% nitrogen) and "y" for the weight of the second fertilizer (12% nitrogen).
So, we have:
- Weight of the first fertilizer (24% nitrogen): x kg
- Weight of the second fertilizer (12% nitrogen): y kg
Step 3: Set up the equation:
The equation is obtained by equating the amount of nitrogen in the mixture to the targeted percentage.
In this case, nitrogen in the first fertilizer + nitrogen in the second fertilizer = nitrogen in the target mixture.
To calculate the nitrogen amount in each fertilizer, we can use the formula:
Nitrogen amount = (Percentage of nitrogen / 100) * Weight
So, the equation becomes:
(0.24 * x) + (0.12 * y) = 0.21 * 100
Step 4: Simplify the equation:
Now, let's simplify the equation by multiplying the percentages and the total weight:
0.24x + 0.12y = 21
Step 5: Solve for one variable in terms of the other:
Since we need to find the specific weights of each fertilizer, we need to express one variable in terms of the other. For example, let's solve for x:
0.24x = 21 - 0.12y
x = (21 - 0.12y) / 0.24
Step 6: Plug in the value found in the equation:
Substitute the value of x back into the equation:
0.24 * [(21 - 0.12y) / 0.24] + 0.12y = 21
Now, you can solve the equation for y by simplifying and solving for y. Once you obtain the value of y, substitute it back into the equation to find the value of x.
Make sure to double-check your solution by verifying that the weights of each fertilizer add up to 100 kg and that the nitrogen percentage is indeed 21%.