You are making iced tea for a friend who prefers it at 80% strength. The function y = (6) (1.0) + x (0.5) 6+x gives the concentration of the tea after adding x fluid ounces of a 50% tea solution to 6 fluid ounces of 100% strength tea. How many fluid ounces of 50% strength tea should you add to 6 fl oz of 100% strength tea?

Question

Mathematics

Irwin

18 June, 00:31

You are making iced tea for a friend who prefers it at 80% strength. The function y = (6) (1.0) + x (0.5) 6+x gives the concentration of the tea after adding x fluid ounces of a 50% tea solution to 6 fluid ounces of 100% strength tea. How many fluid ounces of 50% strength tea should you add to 6 fl oz of 100% strength tea?

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Estrada · Answer 1

You should add 4 fluid ounces of 50% strength tea

Step-by-step explanation:

The actual fuction that gives the final concentration should be:

y=[ (6) (1.0) + x (0.5) ] / (6+x)

Probably it was a typing problem (a missing slash to indicate division). With the function given, the problem has no solution.

We want the strength of the iced tea to be at 80%.

So, to find how many fluid ounces of 50% strength tea (valor of x) you should add, we just need to use the equation of the final concentration with the value of y = 0.8 (y is the concentration of the tea after adding x fluid ounces of 50% strength tea):

0.8 = (6*1 + x*0.5) / (6+x)

0.8 * (6+x) = 6 + 0.5x

4.8 + 0.8x = 6 + 0.5x

0.3x = 1.2

x = 4 fluid ounces