Question

writing and solving inequalities continued
5 helga signs up to coach hockey. she wants to make at least $775 during the season. she gets $200 at the start of the season and $50 for each practice session she has. how many practice sessions does helga need to have this season?
6 logan has a budget of $400 to have family pictures taken. there is a one - time fee of $38. prints cost $25 per page. how many pages of prints can logan order?
7 at toplines 50th anniversary celebration, managers and assistants earn custom - engraved plaques in recognition of their outstanding performance. topline purchased a total of 81 plaques for the event. the company gives 25 plaques to the managers and at least 2 plaques to each assistant. what is the maximum number of assistants at the event?
8 a cartoonist has 150 pieces of original artwork to give to his publishers and some fans who won his online contest. he plans to send 30 drawings to his publishers. he is sending at least 3 pieces of artwork to each contest winner. how many contest winners could there be?

Explanation:

Problem 5:

Step1: Define variable and inequality

Let \( x \) be the number of practice sessions. Helga gets $200 plus $50 per session, and wants at least $775. So the inequality is \( 200 + 50x \geq 775 \).

Step2: Solve for \( x \)

Subtract 200 from both sides: \( 50x \geq 775 - 200 = 575 \). Then divide by 50: \( x \geq \frac{575}{50} = 11.5 \). Since \( x \) must be an integer, \( x \geq 12 \).

Step1: Define variable and inequality

Let \( x \) be the number of print pages. The total cost is $38 (one - time) plus $25 per page, and the budget is $400. So \( 38 + 25x \leq 400 \).

Step2: Solve for \( x \)

Subtract 38: \( 25x \leq 400 - 38 = 362 \). Divide by 25: \( x \leq \frac{362}{25}=14.48 \). Since \( x \) is a number of pages, \( x \leq 14 \).

Step1: Define variable and inequality

Let \( x \) be the number of assistants. Managers get 25 plaques, assistants get at least 2 each, and total plaques are 81. So \( 25+2x \leq 81 \).

Step2: Solve for \( x \)

Subtract 25: \( 2x \leq 81 - 25 = 56 \). Divide by 2: \( x \leq 28 \).

Answer:

12 practice sessions

Problem 6: