To determine how much weight Robert gained during his preparation, we need to calculate the weight gained after the first two months and the weight gained after an additional month. Here are the steps:
1. Initial weight:
- Robert's initial weight was 150 pounds.
2. Weight after two months:
- Two months into the training, Robert weighed [tex]\( 155 \frac{1}{2} \)[/tex] pounds.
- Convert [tex]\( 155 \frac{1}{2} \)[/tex] to a decimal: [tex]\( 155 \frac{1}{2} = 155 + 0.5 = 155.5 \)[/tex] pounds.
3. Weight gain after two months:
- Calculate the weight gain: [tex]\( 155.5 \)[/tex] pounds (weight after two months) [tex]\( - 150 \)[/tex] pounds (initial weight) = 5.5 pounds.
4. Weight after three months:
- After another month, Robert gained an additional [tex]\( 4 \frac{3}{4} \)[/tex] pounds.
- Convert [tex]\( 4 \frac{3}{4} \)[/tex] to a decimal: [tex]\( 4 \frac{3}{4} = 4 + 0.75 = 4.75 \)[/tex] pounds.
- Calculate the weight after the third month: [tex]\( 155.5 \)[/tex] pounds (weight after two months) [tex]\( + 4.75 \)[/tex] pounds (additional gain) = 160.25 pounds.
5. Weight gain after the third month:
- Calculate the weight gain in the third month: [tex]\( 160.25 \)[/tex] pounds (weight after three months) [tex]\( - 155.5 \)[/tex] pounds (weight after two months) = 4.75 pounds.
6. Total weight gain during the preparation:
- Calculate the total weight gain: [tex]\( 5.5 \)[/tex] pounds (gain after two months) [tex]\( + 4.75 \)[/tex] pounds (gain after the third month) = 10.25 pounds.
Therefore, Robert gained a total of 10.25 pounds during his preparation.
The correct answer is:
[tex]\[ 10 \frac{1}{4} \text{ lbs} \][/tex]
