Translate the following into an inequality. Do not solve. Profits in the second quarter for a local retailer were all 112% of that in the first quarter. Profits in the third quarter were 87% of that in the first quarter. The profits for the three quarterscombined exceeded $255,000. What were the profits for each quarter?
1St Qtr profits = $X.
2nd Qtr profits = $1.12X.
3rd Qtr profits = $0.87X.
X + 1.12X + 0.87X > $255,000.
To translate the given information into an inequality, let's assign variables to represent the profits in each quarter.
Let:
- P1 be the profit in the first quarter.
- P2 be the profit in the second quarter.
- P3 be the profit in the third quarter.
According to the information given:
1. Profits in the second quarter were 112% of the first quarter's profit. This can be expressed as: P2 = 1.12P1.
2. Profits in the third quarter were 87% of the first quarter's profit. This can be expressed as: P3 = 0.87P1.
3. The profits for the three quarters combined exceeded $255,000. This can be expressed as: P1 + P2 + P3 > 255,000.
Therefore, the inequality representing the given information is:
P1 + 1.12P1 + 0.87P1 > 255,000.