Let’s say you are buying protein bars for your gym. You have a total of x protein bars. If 10% of the bars are chocolate flavor, 20% are peanut butter flavor, and half of the remaining bars are vanilla flavor, and you have 420 bars in total, how many protein bars do you have in total?
Let's start by finding the number of chocolate flavor bars. We know that 10% of the bars are chocolate flavor, so the number of chocolate flavor bars is 10/100 * x = 0.1 * x.
Similarly, the number of peanut butter flavor bars is 20/100 * x = 0.2 * x.
Now, let's find the number of remaining bars. The remaining bars are x - (0.1 * x + 0.2 * x) = x - 0.3 * x = 0.7 * x.
Half of the remaining bars are vanilla flavor, so the number of vanilla flavor bars is 1/2 * (0.7 * x) = 0.5 * 0.7 * x = 0.35 * x.
Finally, we know that the total number of bars is 420, so x + 0.1 * x + 0.2 * x + 0.35 * x = 420.
This simplifies to 1.65 * x = 420.
Dividing both sides of the equation by 1.65, we find x = 420 / 1.65 = 254.55 (rounded to two decimal places).
Therefore, you have a total of approximately 254 protein bars.