Question

Write an inequality to represent each situation.

1. The cost to run an ad in a newspaper is $10 plus $0.25 per word. What is the maximum number of words Mrs. Kiehl can put in her ad if the most she can spend is $15?
2. You spent $70 for a program to help you develop a phone app. You can sell the app for $5 per download. You want to earn a profit of at least $1000. What is the minimum number of downloads you need?

Answer 1

1. The maximum number of words Mrs. Kiehl can put in her ad is 20. 2. The minimum number of downloads needed to earn a profit of at least $1000 is 214.

Step-by-step explanation:

1. Let x be the number of words Mrs. Kiehl can put in her ad. The cost to run the ad is $10 plus $0.25 per word. So the total cost of the ad is 10 + 0.25x. The most she can spend is $15. Therefore, we can write the inequality as:

10 + 0.25x ≤ 15

To find the maximum number of words Mrs. Kiehl can put in her ad, we can solve this inequality by subtracting 10 from both sides:

0.25x ≤ 5

Then, we divide both sides by 0.25:

x ≤ 20

So, the maximum number of words Mrs. Kiehl can put in her ad is 20.

2. Let x be the number of downloads. The cost to develop the app is $70 and the app can be sold for $5 per download. The profit for x number of downloads is given by 5x - 70. The minimum number of downloads needed to earn a profit of at least $1000 can be found by setting the profit equation greater than or equal to 1000:

5x - 70 ≥ 1000

Adding 70 to both sides, we get:

5x ≥ 1070

Then, dividing both sides by 5, we have:

x ≥ 214

So, the minimum number of downloads needed to earn a profit of at least $1000 is 214.