SOLUTION: A yogurt company blends regular yogurt that is 4% fat with its no-fat yogurt to obtain low-fat yogurt that is 1% fat. How many pounds of non-fat yogurt must be mixed to obtain 60 p
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Question 615814: A yogurt company blends regular yogurt that is 4% fat with its no-fat yogurt to obtain low-fat yogurt that is 1% fat. How many pounds of non-fat yogurt must be mixed to obtain 60 pounds of low-fat yogurt?
Found 2 solutions by scott8148, dragonwalker:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
(0%)(x) + (4%)(60 - x) = (1%)(60)
Answer by dragonwalker(73) (Show Source): You can put this solution on YOUR website!
(note * symbol used for multiplication sign so as not to confuse the algebra unit x)
Firstly you want to look at what you know.
1) There will be a final product of 60lbs of yogurt
2) There are two types of yogurt, one that is 0% fat and the other 4% (which can also be written as 0.04 (4/100)
The 4% fat has a greater amount of fat than the final product of 1% (+3)
The 0% fat has a lesser amount of fat than the final product of 1% (-1)
So for every unit of 4% we need to lower it by 3 to get the 1%.
How can we lower it by 3? Well one unit of 0% fat would lower by one (-1), so 3 units of 0% would lower it by 3?
So for 1 unit of 4% we need to add 3 units of 0% (a total of 4).
So now we need to see how big one of these units is.
We need a total of 4 units to mix the yogurt correctly so we need to see how many times 4 goes into 60 lbs. Let us say that x is the size of one unit so:
4x = 60
x = 60/4
x = 15
so each unit is 15 lbs
So how many units of 4% did we need? 1 unit (or 1x).
so: 1x = 1 * 15
= 15 lbs
How much 0% did we need? 3 units.
So 3 units (or 3x) = 3 * 15
= 45
So we need 45 lbs of 0%
So we need 15 lbs of 4% and 45 lbs of 0%
To check:
we know x = 15
so if we decide to multiply the amounts with the concentrations then we should end up with a balanced equation.
How much fat in 60 lbs of 1 %?
1 % is one hundredth or 1/100 = 0.01
so the amount of fat is 60 * 0.01 = 0.6 lbs of fat
4% is 4/100 = 0.04
So 0.04 * 15 = 0.6 lbs of fat!!!
The 0% yogurt doesn't add any fat, but just makes the weight up to 60 lbs.
However although finding out how much fat you need in the final product and then working out how to get that amount of fat using the 4% would work for this, the other method is needed if both yogurts being mixed have some fat.
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