Question: User: S.16 Compare ratios: word problems 2HT
Every year, Jada's scout troop makes and sells tie-dyed shirts to raise money for charity.
Short-sleeved shirts are easier to make, so they try to sell more short-sleeved shirts than
long-sleeved shirts. Last year, her troop sold 20 short-sleeved shirts and 25 long-sleeved
shirts. This year, her troop sold 35 short-sleeved shirts and 50 long-sleeved shirts. Which
year's sales had a greater ratio of short-sleeved shirts to long-sleeved shirts?
Last year's sales had a greater ratio.
This year's sales had a greater ratio.
Neither. Jada's troop sold the same ratio in both years.
1. **State the problem:** We need to compare the ratio of short-sleeved shirts to long-sleeved shirts sold last year and this year.
2. **Write the ratios:**
- Last year's ratio: $$\frac{20}{25}$$
- This year's ratio: $$\frac{35}{50}$$
3. **Simplify each ratio:**
- Last year: $$\frac{20}{25} = \frac{\cancel{5} \times 4}{\cancel{5} \times 5} = \frac{4}{5}$$
- This year: $$\frac{35}{50} = \frac{\cancel{5} \times 7}{\cancel{5} \times 10} = \frac{7}{10}$$
4. **Compare the simplified ratios:**
- Convert to decimals for easier comparison:
- Last year: $$\frac{4}{5} = 0.8$$
- This year: $$\frac{7}{10} = 0.7$$
5. **Conclusion:** Since $$0.8 > 0.7$$, last year's sales had a greater ratio of short-sleeved to long-sleeved shirts.
**Final answer:** Last year's sales had a greater ratio.