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?

Answer 1

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.