Solving & Graphing Multi-Step Inequalities Challenge

A store sells notebooks for $2 each and pens for $1 each. If you want to spend no more than $20 on notebooks and pens combined, write and solve the inequality for the number of notebooks (n) and pens (p) you can buy. Graph the solution on a number line.

• The maximum number of pens is 20, regardless of notebooks.

• You can only buy 5 notebooks and no pens.

• The number of notebooks (n) can be from 0 to 10, and for each n, the number of pens (p) can be from 0 to (20 - 2n).

• You can buy up to 15 notebooks and 5 pens.

Maria has $50 to spend on books and magazines. If each book costs $8 and each magazine costs $5, write an inequality to represent the maximum number of books and magazines she can buy. Solve the inequality and graph the solution on a number line.

• 8x + 5y = 50

• The maximum number of books and magazines Maria can buy is represented by the inequality 8x + 5y ≤ 50, with integer solutions for (x, y) being (0,10), (1,9), (2,8), (3,7), (4,6), (5,5), (6,2).

• x + y ≤ 10

• 8x + 5y < 50

A gym charges a $30 membership fee plus $5 per class. If you want to spend no more than $100 in a month, write and solve the inequality for the number of classes (c) you can attend. Graph the solution on a number line.

• c ≤ 12

• c ≤ 14

• c ≤ 10

• c ≤ 20

A farmer has a budget of $200 to buy seeds and fertilizer. If each bag of seeds costs $15 and each bag of fertilizer costs $10, write an inequality to represent the maximum number of bags of seeds (s) and fertilizer (f) he can buy. Solve the inequality and graph the solution on a number line.

• 15s + 10f ≤ 200; s ≤ 13, f ≤ 20.

• 20s + 5f ≤ 200; s ≤ 10, f ≤ 40.

• 5s + 20f ≤ 200; s ≤ 30, f ≤ 5.

• 10s + 15f ≤ 200; s ≤ 20, f ≤ 10.

A concert ticket costs $50, and you want to buy tickets for your friends without spending more than $300. Write and solve the inequality for the number of tickets (t) you can buy. Graph the solution on a number line.

• t = 5

• t < 6

• t >= 7

• t <= 6

A school is planning a field trip and has a budget of $400. If each bus costs $100 and each ticket costs $20, write an inequality to represent the maximum number of buses (b) and tickets (t) they can purchase. Solve the inequality and graph the solution on a number line.

• 100b + 20t ≤ 400, where 0 ≤ b ≤ 4 and t ≤ 20 - 5b.

• 100b + 30t ≤ 400

• 50b + 10t ≤ 400

• 200b + 20t ≤ 400

You are saving money for a new video game that costs $60. If you save $5 a week, write an inequality to determine how many weeks (w) it will take to save enough money. Solve the inequality and graph the solution on a number line.

• w < 12

• w > 15

• w <= 10

• w >= 12

A family is planning a vacation and has a budget of $1,200. If they plan to spend $300 on flights and $150 per day on accommodations, write an inequality to represent the maximum number of days (d) they can stay. Solve the inequality and graph the solution on a number line.

• d <= 5

• d <= 4

• d <= 6

• d <= 8

A charity event has a goal of raising at least $1,000. If each ticket sold is $20 and they have already raised $300 from donations, write and solve the inequality for the number of tickets (t) they need to sell. Graph the solution on a number line.

• t >= 35

• t >= 25

• t <= 40

• t < 35

A student has a budget of $100 for school supplies. If notebooks cost $3 each and folders cost $2 each, write an inequality to represent the maximum number of notebooks (n) and folders (f) the student can buy. Solve the inequality and graph the solution on a number line.

• 3n + 2f < 100

• n + 3f ≤ 100

• 4n + f ≤ 100

• 3n + 2f ≤ 100