Calculating Total Toys Manufactured Over Three Years
This problem requires us to calculate the total number of toys manufactured by a machine over three specific years: 2018, 2019, and 2020. We are given the initial production in 2018 and the percentage changes for the subsequent two years.
Step 1: Production in 2018
The number of toys manufactured in 2018 is given directly:
Production in 2018 = 25,000 toys
Step 2: Calculate Production in 2019
In 2019, the production increased by 20% compared to 2018. To find the production in 2019, we first calculate the increase amount and then add it to the 2018 production.
- Increase in production = 20% of 25,000
- Increase = $\frac{20}{100} \times 25,000$
- Increase = $0.20 \times 25,000$
- Increase = 5,000 toys
Now, add this increase to the 2018 production:
Production in 2019 = Production in 2018 + Increase
Production in 2019 = $25,000 + 5,000$
Production in 2019 = 30,000 toys
Alternatively, we can calculate this as 120% of the 2018 production:
Production in 2019 = $25,000 \times (1 + \frac{20}{100}) = 25,000 \times 1.20 = 30,000$ toys
Step 3: Calculate Production in 2020
In 2020, the production decreased by 15% due to a strike. This decrease is based on the 2019 production figure.
- Decrease in production = 15% of 30,000
- Decrease = $\frac{15}{100} \times 30,000$
- Decrease = $0.15 \times 30,000$
- Decrease = 4,500 toys
Now, subtract this decrease from the 2019 production:
Production in 2020 = Production in 2019 - Decrease
Production in 2020 = $30,000 - 4,500$
Production in 2020 = 25,500 toys
Alternatively, we can calculate this as 85% (100% - 15%) of the 2019 production:
Production in 2020 = $30,000 \times (1 - \frac{15}{100}) = 30,000 \times 0.85 = 25,500$ toys
Step 4: Calculate Total Toys Manufactured
Finally, to find the total number of toys manufactured in the three years, we sum the production figures for 2018, 2019, and 2020.
Total Toys = Production in 2018 + Production in 2019 + Production in 2020
Total Toys = $25,000 + 30,000 + 25,500$
Total Toys = 80,500 toys
Summary Table
| Year | Initial Production / Previous Year Production | Percentage Change | Calculated Production |
|---|---|---|---|
| 2018 | - | - | 25,000 |
| 2019 | 25,000 (from 2018) | +20% | 30,000 |
| 2020 | 30,000 (from 2019) | -15% | 25,500 |
| Total | - | - | 80,500 |
Therefore, the total number of toys manufactured by the machine in the three years is 80,500.
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