How much alfalfa should be added to 60L of ostrich pellets to create a mix that is 32% alfalfa by volume?
I have no idea how to start this question. If I let x be the alfalfa and x+60 = 32 be the mix
60/68*32 = 28.23L
To solve this question, you can set up the equation representing the volume of alfalfa in the mix. Let's assume the volume of alfalfa to be added is represented by x liters.
According to the information given, the volume of ostrich pellets is 60L, and the desired mix is 32% alfalfa by volume. This means that the volume of alfalfa in the mix should be 32% of the total mix volume.
The equation can be set up as follows:
x / (x + 60) = 0.32
To solve this equation, you can use the following steps:
1. Multiply both sides of the equation by (x + 60) to eliminate the denominator:
x = 0.32 * (x + 60)
2. Distribute 0.32 to both terms on the right side:
x = 0.32x + 0.32 * 60
3. Simplify and combine like terms:
x = 0.32x + 19.2
4. Subtract 0.32x from both sides to isolate the x term:
x - 0.32x = 19.2
0.68x = 19.2
5. Divide both sides by 0.68 to solve for x:
x = 19.2 / 0.68
x ≈ 28.24
Therefore, approximately 28.24L of alfalfa should be added to the 60L of ostrich pellets to create a mix that is 32% alfalfa by volume.
To solve this problem, let's break it down step by step. We'll start by defining the variables:
Let:
x = the amount of alfalfa added (in liters)
Now, let's establish the information we have:
1. We want to create a mix that is 32% alfalfa by volume.
2. We currently have 60 liters of ostrich pellets.
Next, we can set up an equation based on the given information:
The amount of alfalfa in the final mix will be x liters, and the total volume of the final mix will be (x + 60) liters.
Since we want the mix to be 32% alfalfa, we can write the equation as:
x / (x + 60) = 0.32
To solve this equation, we can cross-multiply:
x = 0.32 * (x + 60)
Distribute 0.32 to the terms inside the parentheses:
x = 0.32x + 0.32 * 60
Simplify the right side of the equation:
x = 0.32x + 19.2
Now, let's isolate x by moving 0.32x to the left side:
x - 0.32x = 19.2
Combine like terms:
0.68x = 19.2
Finally, solve for x by dividing both sides by 0.68:
x = 19.2 / 0.68
By evaluating this expression, we find that x is equal to approximately 28.24 liters.
Therefore, approximately 28.24 liters of alfalfa should be added to the 60 liters of ostrich pellets to create a mix that is 32% alfalfa by volume.
a / (a + 60) = .32
a = .32 a + 19.2
.68 a = 19.2