Question

jacob put hummingbird feeders in his garden. to make the food for his small feeder, he mixed sugar with warm water. he used the same amount of sugar for his large feeder, but he added more water to completely fill it. which mixture was sweeter? the small feeders mixture was sweeter. the large feeders mixture was sweeter. neither. the mixtures were equally sweet.

Explanation:

Step1: Define sweetness by sugar - water ratio

Sweetness depends on the proportion of sugar in the mixture. Let the amount of sugar be $s$. Let the amount of water in the small - feeder be $w_1$ and in the large - feeder be $w_2$ where $w_2>w_1$.

Step2: Calculate sugar - water ratios

The sugar - water ratio for the small feeder is $\frac{s}{w_1 + s}$, and for the large feeder is $\frac{s}{w_2 + s}$.

Step3: Compare the ratios

Since $w_2>w_1$, we have $\frac{s}{w_1 + s}>\frac{s}{w_2 + s}$. A higher sugar - water ratio means a sweeter mixture.

Answer:

The small feeder's mixture was sweeter.