A nontoxic wood furniture polish can be made by mixing mineral(or olive)oil with vinegar. To make a 16-oz batch for a squirt bottle, Michael uses an amount of mineral oil that is 4oz more than twice the amount of vinegar. How much of each ingredient is required?
v + (4+2v) = 16
v = 4
so, 4 oz vinegar and 12 oz oil.
To determine the amounts of mineral oil and vinegar needed, we can set up an equation based on the problem.
Let x be the amount of vinegar in ounces.
Twice the amount of vinegar would be 2x.
And 4 ounces more than that would be 2x + 4.
According to the problem, the amount of mineral oil is 4 ounces more than twice the amount of vinegar.
So the equation is:
2x + 4 = amount of mineral oil (in ounces)
Since we are making a 16-ounce batch, the sum of the amounts of vinegar and mineral oil should equal 16.
Therefore:
x + (2x + 4) = 16
Simplifying the equation:
3x + 4 = 16
3x = 16 - 4
3x = 12
x = 12 / 3
x = 4
So, we need 4 ounces of vinegar and 2x + 4 ounces of mineral oil.
Substituting the value of x into the equation:
2(4) + 4 = 8 + 4 = 12
Therefore, we need 4 ounces of vinegar and 12 ounces of mineral oil to make a 16-ounce batch of nontoxic wood furniture polish.
To solve this problem, we need to set up equations based on the given information.
Let's assume the amount of vinegar used is V ounces. According to the problem, Michael uses an amount of mineral oil that is 4 ounces more than twice the amount of vinegar. Therefore, the amount of mineral oil he uses can be represented as 2V + 4 ounces.
We are also given that the total batch size is 16 ounces, which means the amount of vinegar and mineral oil used must add up to 16 ounces. So we can set up an equation:
V + (2V + 4) = 16
Simplifying the equation:
3V + 4 = 16
Subtracting 4 from both sides:
3V = 12
Dividing both sides by 3:
V = 4
Now that we know V (vinegar) is 4 ounces, we can substitute this value back into the equation we initially set up to find the amount of mineral oil:
2V + 4 = 2(4) + 4 = 8 + 4 = 12
Therefore, Michael needs 4 ounces of vinegar and 12 ounces of mineral oil to make a 16-oz batch of nontoxic wood furniture polish.