Question is a word problem so its below

Question

cake batter frozen yogurt costs $0.60/oz and chocolate frozen yogurt costs $0.40/oz. if you want to buy 6 oz of frozen yogurt for an average of $0.45/oz, how many of each flavor should you get

Answer 1

They want you to find out how much of each flavor you need, so set up variable for each number:

 

x = number of ounces of cake batter frozen yogurt

y = number of ounces of chocolate frozen yogurt

 

The first thing you know is that x + y = 6, because you want to buy a total of 6 ounces

 

Now try to figure out the price of the frozen yogurt you are planning to buy.

 

0.6x is the cost of the cake batter frozen yogurt you buy

0.4y is the cost of the chocolate frozen yogurt you buy

 

So 0.6x + 0.4y is the total amount of money you spend.

 

If you want the AVERAGE cost to be $0.45, then the total cost divided by the total amount would have to be 0.45.

 

So (0.6x + 0.4y) / (x + y) = 0.45.   But we know that x + y = 6, so we can use 6 for the total amount instead of x + y.  So that gives us a second equation:

 

(0.6x + 0.4y) / 6 = 0.45

 

Multiplying both sides by 6 gives us a simpler equation:

0.6x + 0.4y = 27

 

So we have two equations to solve:

 

0.6x + 0.4y = 2.7

x + y = 6

 

Multiply both sides of the second equation by 0.4:

.4x + .4y = 2.4

 

Subtract this equation from the other equation to eliminate y:

.2x = .3

 

Divide both sides by .2:

x = 1.5

 

Since x + y = 6, that means that y must be 4.5.

 

So you would buy 1.5 ounces of cake batter frozen yogurt and 4.5 ounces of chocolate frozen yogurt