Question

Which of the following are solutions to 10.50x + 5.50y + 150 ≤ 300

(2, 20)

(2, -5)

(0, 28)

(6, 15)

(10, 30)

Answer 1

To determine which of the given pairs \((x, y)\) are solutions to the inequality \(10.50x + 5.50y + 150 ≤ 300\), we can simplify the inequality first:

1. Subtract 150 from both sides:

\[
10.50x + 5.50y ≤ 150
\]

Now we will evaluate each pair to see if they satisfy the inequality.

**1. For \((2, 20)\):**

\[
10.50(2) + 5.50(20) = 21 + 110 = 131
\]
Since \(131 ≤ 150\), this pair is a solution.

**2. For \((2, -5)\):**

\[
10.50(2) + 5.50(-5) = 21 - 27.5 = -6.5
\]
Since \(-6.5 ≤ 150\), this pair is a solution.

**3. For \((0, 28)\):**

\[
10.50(0) + 5.50(28) = 0 + 154 = 154
\]
Since \(154 ≤ 150\) is not true, this pair is **not** a solution.

**4. For \((6, 15)\):**

\[
10.50(6) + 5.50(15) = 63 + 82.5 = 145.5
\]
Since \(145.5 ≤ 150\), this pair is a solution.

**5. For \((10, 30)\):**

\[
10.50(10) + 5.50(30) = 105 + 165 = 270
\]
Since \(270 ≤ 150\) is not true, this pair is **not** a solution.

**Summary of solutions:**

The pairs that are solutions to the inequality are:

- \((2, 20)\)
- \((2, -5)\)
- \((6, 15)\)

Thus, the final result is:

- \((2, 20)\)
- \((2, -5)\)
- \((6, 15)\)