Ziggy’s Famous Yogurt blends regular
yogurt that is 3% fat with its no-fat yogurt to obtain lowfat
yogurt that is 1% fat. How many pounds of regular yogurt and how many pounds of no-fat yogurt should be mixed to obtain 60 pounds of low-fat yogurt
To solve this problem, we need to set up a system of equations to represent the given information.
Let's assume:
Let x be the number of pounds of regular yogurt (3% fat).
Let y be the number of pounds of no-fat yogurt (0% fat).
According to the information given, Ziggy's Famous Yogurt blends regular yogurt (3% fat) with no-fat yogurt to obtain low-fat yogurt (1% fat). This means that the fat content of the blended yogurt is an average of the fat contents of the two types of yogurt.
To find the number of pounds of each type of yogurt needed to obtain 60 pounds of low-fat yogurt (1% fat), we can set up the following equations:
Equation 1: x + y = 60 (equation representing the total weight of the yogurt)
Equation 2: (0.03x + 0.00y) / 60 = 0.01 (equation representing the fat content of the blended yogurt)
Let's solve this system of equations.
From Equation 1: x + y = 60
Rearrange the equation to express y in terms of x: y = 60 - x
Substitute this expression for y in Equation 2 and solve for x:
(0.03x + 0.00(60 - x)) / 60 = 0.01
(0.03x + 0) / 60 = 0.01
Multiply both sides of the equation by 60:
0.03x = 0.01 * 60
0.03x = 0.6
Divide both sides of the equation by 0.03:
x = 0.6 / 0.03
x = 20
Now, substitute this value of x back into Equation 1 to find the value of y:
20 + y = 60
y = 60 - 20
y = 40
Therefore, 20 pounds of regular yogurt and 40 pounds of no-fat yogurt should be mixed to obtain 60 pounds of low-fat yogurt.