Certainly! Let's solve this step-by-step:
1. Understand the problem:
- We know that consuming 114 grams of carbohydrates provides 38% of the daily recommended value.
- We need to determine how many grams of carbohydrates would provide 100% of the daily recommended value.
2. Set up a proportion:
- We can set up a proportion to find the number of grams needed for 100% of the daily recommended value.
- Let's denote [tex]\( x \)[/tex] as the grams of carbohydrates needed for 100% of the daily recommended value.
3. Formulate the proportion:
- The proportion based on the given information would be:
[tex]\[
\frac{114 \text{ grams}}{38\%} = \frac{x \text{ grams}}{100\%}
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- Cross-multiply to solve for [tex]\( x \)[/tex]:
[tex]\[
114 \text{ grams} \times 100 = 38 \times x
\][/tex]
- Simplify the equation:
[tex]\[
11400 = 38x
\][/tex]
- Divide both sides by 38 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{11400}{38}
\][/tex]
[tex]\[
x = 300 \text{ grams}
\][/tex]
So, you would need to eat 300 grams of carbohydrates in a day to reach the daily recommended value of 100%.
