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An electric filter purifies air at the rate of

\[35\] liters per minute and uses energy at the rate of
\[0.8\] Joules per minute. It also purifies water at the rate of
\[25\] liters per minute and uses energy at the rate of
\[1.3\] Joules per minute.
The filter is expected to purify more than
\[1000\] liters of air and water while using less than
\[170\] Joules of energy.
Let
\[A\] denote the number of minutes it spends purifying air and
\[W\] the number of minutes it spends purifying water.
Write an inequality that represents the condition based on the number of liters of air and water.
Write an inequality that represents the condition based on the number of Joules of energy.

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 hours ago

To represent the conditions based on the purification of air and water as well as the energy consumption, we'll set up the inequalities as follows:

1. **Condition based on the number of liters of air and water:**
- The filter purifies air at a rate of \(35\) liters per minute, so in \(A\) minutes, it purifies \(35A\) liters of air.
- The filter purifies water at a rate of \(25\) liters per minute, so in \(W\) minutes, it purifies \(25W\) liters of water.
- The total amount of air and water purified should be more than \(1000\) liters.

The inequality representing this condition is:
\[
35A + 25W > 1000
\]

2. **Condition based on the energy consumption:**
- The filter uses energy at a rate of \(0.8\) Joules per minute for air purification, so in \(A\) minutes, it uses \(0.8A\) Joules of energy.
- The filter uses energy at a rate of \(1.3\) Joules per minute for water purification, so in \(W\) minutes, it uses \(1.3W\) Joules of energy.
- The total energy used should be less than \(170\) Joules.

The inequality representing this condition is:
\[
0.8A + 1.3W < 170
\]

Thus, the two inequalities that represent the conditions are:
1. \(35A + 25W > 1000\)
2. \(0.8A + 1.3W < 170\)