Two-Variable Inequalities

Your school is hosting a spaghetti dinner as a fundraiser. You estimate 200 adults and 250 children will attend. Let x be the cost of adult tickets and y the cost of a child ticket. Write an inequality to represent what ticket prices to set to raise at least $3200.

• x + y ≥ 3200

• 250x + 200y ≥ 3200

• 200x + 250y ≤ 3200

• 200x + 250y ≥ 3200

You are running the concession stand at a basketball game. You sell hot dogs for $2 and sodas for $0.75.  To cover overhead expenses, you need to make more than $180.  Write an inequality to find how many hot dogs and sodas you need to sell. Let x equal the number of hot dogs and y equal the number of sodas.

• y > x + 180

• x + y > 180

• 0.75x + 2y > 180

• 2x + 0.75y > 180

A jewelry designer is making beaded jewelry with the 835 beads she currently has in stock. Bracelets, x, use 15 beads and necklaces, y, use 80 beads. Select the inequality that describes the situation.

• 15x + 80y ≤ 835

• 15x - 80y ≤ 835

• 15x * 80y ≥ 835

• 15x + 80y ≥ 835

Belton is hosting a festival where vendors can pay to have a small booth or a large booth. The fee for a small booth is $85, and the fee for a large booth is $200. The city hopes to receive at least $3,700 in fees. Which inequality models this situation? Let x equal the number of small booths and y the number of large.

• 3700 - 200y = 85x

• 200y - 85x > 3700

• 85x + 200y ≥ 3700

• 85x + 200y ≤  3700

• Astrid meets both of her expectations

• Astrid buys the expected number of fruits, but she does beyond her budget

• Astrid stays within her budget, but she doesn't buy the expected number of fruits

• Astrid doesn't meet either of her expectations

• Lars meets both of his expectations

• Lars works for the expected number of days but doesn't earn the expected number of money

• Lars earns the expected amount of money but doesn't work for the expected number of days

• Lars doesn't meet either of his expectations

Nina is playing arcade games that take tokens. She can afford to buy up to 26 tokens. Skee ball requires 1 token per game and pinball requires 2 tokens per game. Select the inequality in standard form that describes this situation. Use x for the number of skee ball games and y for the number of pinball.

• x + 2y ≤ 26

• x + 2y ≥ 26

• 2x + y ≥ 26

• 2x + y ≤ 26

Allen enjoys gardening. Every sunflower plant he waters requires 0.7 liters of water, and every rose bush he waters requires 0.5 liters of water. Allen has a total 11 liters of water for these plants.  Write an inequality to represent the situation.

• 0.7s - 0.5r ≥ 11

• 0.7s + 0.5r ≥ 11

• 0.7s + 0.5r ≤ 11

• 0.7r + 0.5s ≤ 11

Carolyn bought a dress that cost $45 and several pairs of pants, p, that were $9.99 each.  Michelle bought a jacket for $30 and pants that cost $11.50 each.  How many pairs of pants would the girls have to buy for Michelle’s total to exceed Carolyn’s total?

• 45 + 30 > 9.99p + 11.50p 

• 45p + 9.99 > 30p + 11.50

• 45 + 9.99p < 30 + 11.50p

• 45 + 9.99p > 30 + 11.50p

Is (-2, 4) a solution to this inequality?

• Yes

• No