Question

write and solve an inequality for each problem.

1. ian wants to promote his band on the internet. site a offers website hosting for $4.95 per month with a $49.95 startup fee. site b offers website hosting for $9.95 per month with no startup fee. for how many months would ian need to keep the website for site b to be less expensive than site a?

1. for what values of x is the area of the rectangle greater than the perimeter?

copyright by holt, rinehart and winston
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36
holt algebra 1

Explanation:

Problem 12

Step1: Define variables and costs

Let \( m \) be the number of months.
Cost for Site A: \( 49.95 + 4.95m \)
Cost for Site B: \( 9.95m \)

Step2: Set up inequality

We want Site B to be less expensive than Site A:
\( 9.95m < 49.95 + 4.95m \)

Step3: Solve the inequality

Subtract \( 4.95m \) from both sides:
\( 9.95m - 4.95m < 49.95 \)
\( 5m < 49.95 \)

Divide both sides by 5:
\( m < \frac{49.95}{5} \)
\( m < 9.99 \)

Since \( m \) represents months (a positive integer), \( m \leq 9 \) months. But for Site B to be strictly less expensive, we consider \( m < 10 \) (since at \( m = 10 \), Site A: \( 49.95 + 4.95(10) = 99.45 \), Site B: \( 9.95(10) = 99.5 \), so at \( m = 10 \), Site A is cheaper. Wait, recalculate:

Wait, \( \frac{49.95}{5} = 9.99 \), so \( m < 9.99 \), so for \( m \leq 9 \) months, Site B is less expensive? Wait no, let's check \( m = 10 \):

Site A: \( 49.95 + 4.95(10) = 49.95 + 49.5 = 99.45 \)
Site B: \( 9.95(10) = 99.5 \)
So at \( m = 10 \), Site A is cheaper. At \( m = 9 \):

Site A: \( 49.95 + 4.95(9) = 49.95 + 44.55 = 94.5 \)
Site B: \( 9.95(9) = 89.55 \)
So Site B is cheaper at \( m = 9 \), and at \( m = 10 \), Site A is cheaper. Wait, my calculation for \( \frac{49.95}{5} \) is 9.99, so \( m < 9.99 \), so the number of months must be less than 10. So for \( m = 1, 2, ..., 9 \), Site B is cheaper. For \( m \geq 10 \), Site A is cheaper.

Problem 13

Step1: Recall area and perimeter formulas

Area of rectangle: \( A = \text{length} \times \text{width} = 7(x + 2) \)
Perimeter of rectangle: \( P = 2(\text{length} + \text{width}) = 2(7 + x + 2) = 2(x + 9) = 2x + 18 \)

Step2: Set up inequality

We want area > perimeter:
\( 7(x + 2) > 2x + 18 \)

Step3: Solve the inequality

Expand left side:
\( 7x + 14 > 2x + 18 \)

Subtract \( 2x \) from both sides:
\( 5x + 14 > 18 \)

Subtract 14 from both sides:
\( 5x > 4 \)

Divide by 5:
\( x > \frac{4}{5} \)
\( x > 0.8 \)

Answer:

s:

1. Ian needs to keep the website for less than 10 months (specifically \( m < 10 \), or \( m \leq 9 \) if considering whole months).
2. \( x > \frac{4}{5} \) (or \( x > 0.8 \))