Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. Sheldon combines an amount of the two cereals in a single bowl of mixed cereal that is 65% fiber. If the bowl contains a total of 12 ounces of cereal, how much of the cereal, in ounces, is Fiber X?

There are 4 ounces of Fiber X cereal in the mix

Step-by-step explanation:

Lets n be the amount of ounces of Fiber X in the mix. Since there are a total of 12 ounces in the mix, then, on terms of n, there are 12-n ounces of Fiber Max on it.

Since 65% of the mix is Fiber, then there are 12*0.65 = 7.8 ounces of Fiber. We can also obtain this value if we take the proportions of Fiber in each cereal of the mix (in terms of n), so that we can obtain the true value of n

we have

7.8 = n * 0.55 + (12-n) * 0.7 = 0.55n + 8.4 - 0.7 n = 8.4-0.15n

Therefore

0.15 n = 0.6

n = 0.6/0.15 = 4

As a consecuence, there are 4 ouces of Fiber X cereal in the mix.