To find out how much sugar is needed when the ratio of flour to sugar is [tex]\( 5:3 \)[/tex] and we have 200 grams of flour, we can follow these steps:
1. Understand the ratio: The ratio [tex]\( 5:3 \)[/tex] means for every 5 parts of flour, there are 3 parts of sugar.
2. Set up the proportion: We need to find out how many grams of sugar correspond to 200 grams of flour. Let [tex]\( F \)[/tex] be the amount of flour and [tex]\( S \)[/tex] be the amount of sugar. The ratio can be written as:
[tex]\[
\frac{F}{S} = \frac{5}{3}
\][/tex]
3. Substitute the given amount of flour:
[tex]\[
\frac{200}{S} = \frac{5}{3}
\][/tex]
4. Solve the proportion:
- Cross-multiply to solve for [tex]\( S \)[/tex]:
[tex]\[
200 \times 3 = 5 \times S
\][/tex]
[tex]\[
600 = 5S
\][/tex]
- Divide both sides by 5 to find [tex]\( S \)[/tex]:
[tex]\[
S = \frac{600}{5}
\][/tex]
[tex]\[
S = 120
\][/tex]
5. Conclusion: The amount of sugar needed is 120 grams.
Therefore, the correct answer is:
(A) 120 g
