Question

Charlie's horse, Star, was getting too heavy eating 3 1/2
pounds of horse feed twice a day. Charlie reduced Star's feed by 3/4
of a pound at each feeding. How much is Star now eating each day? You must type your response as a simplified mixed number

Answer 1

Star was originally eating \( 3 \frac{1}{2} \) pounds of horse feed at each feeding.

First, let's convert \( 3 \frac{1}{2} \) to an improper fraction.

\[
3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2}
\]

Since Star was fed twice a day, the total daily feed was:

\[
2 \times \frac{7}{2} = \frac{14}{2} = 7 \text{ pounds}
\]

Now, Charlie reduced Star's feed by \( \frac{3}{4} \) pound at each feeding. To find how much Star is now eating at each feeding, we subtract \( \frac{3}{4} \) from \( \frac{7}{2} \):

Convert \( \frac{7}{2} \) to have a common denominator with \( \frac{3}{4} \).

The least common multiple of 2 and 4 is 4. So,

\[
\frac{7}{2} = \frac{7 \times 2}{2 \times 2} = \frac{14}{4}
\]

Now we can perform the subtraction:

\[
\frac{14}{4} - \frac{3}{4} = \frac{14 - 3}{4} = \frac{11}{4}
\]

Now, to find Star's total daily feed:

\[
2 \times \frac{11}{4} = \frac{22}{4} = \frac{11}{2} \text{ pounds}
\]

Now, convert \( \frac{11}{2} \) to a mixed number:

\[
\frac{11}{2} = 5 \frac{1}{2}
\]

Thus, Star is now eating a total of \( 5 \frac{1}{2} \) pounds of horse feed each day.

The final answer is:

\[
\boxed{5 \frac{1}{2}}
\]