# How many cup of juice must be added to 30 cup of punch that is 8% grapefruit juice, to obtain a punch that is 10% grapefruit?

Apr 19, 2018

$\left(\frac{8}{100}\right) \cdot 30 = 2.4$ cups
So the other components of the punch are going to remain constant. Therefore, you have $30 - 2.4$ cups ($27.6$ cups) of other components. $27.6$ are 92% of the current punch. You want them to be 90%. Therefore, $x \cdot \left(\frac{90}{100}\right) = 27.6$,
Therefore, $x = 27.6 \cdot \left(\frac{100}{90}\right) = 30.67$. Therefore, the answer is $0.67$ cups of grapefruit.