2.7 Writing Linear Inequalities in Two Variables

The difference between Connie’s height (c) and Janet’s height (j) is not more than 1 foot and 6 inches. Which of the following expressions best describes the height of the two girls?

Janel purchased three apples (a) and two oranges (o). Her whole payment was NO more than 123 pesos. Which of the algebraic expressions below best represents Janel's purchases?

Kim is using two mobile networks. Network one charges RM0.30 for every minute of call and network two charges RM0.38 for every minute of call. Kim spends at least RM68 monthly for calls. Which of the following inequalities is best to represent Kim's situation?

• 0.30x + 0.38y < 68

• 0.30x + 0.38y > 68

• 0.30x + 0.38y ≤ 68

• 0.30x + 0.38y ≥ 68

Jarena paid less than PHP 600 in total for 5 kilos of rice (r) and 2 kilos of fish (f) at the market. Which of the following algebraic expressions best describes Jarena's total spending at the market?

Yumi is determining the seating arrangement for her big dinner party. Circular tables will seat 8 guests and rectangular tables can seat 10 guests. Yumi is informed that at least 162 guests are attending.

Write an inequality that describes the situation.

Let x = # of circular tables

Let y = # of rectangular tables

• 8x + 10y < 162

• 8x + 10y ≤ 162

• 8x + 10y > 162

• 8x + 10y ≥ 162

Write the linear inequality in standard form for this situation: Ms. Savva is ordering pizzas and breadsticks for a school party and has a budget of no more than RM81. An order of breadsticks costs RM7 and a pizza costs RM13.

• 7x + 13y < 81

• 7x + 13y ≤ 81

• 7x + 13y ≥ 81

• 7x + 13y > 81

Justin charges RM11 to mow a small lawn and RM26 to mow a large lawn. He would like to make at least RM130.

Write an inequality that describes the situation.

Let x = # of small lawns mowed and

Let y = # of large lawns mowed

• 11x + 26y ≥ 130

• 11x + 26y > 130

• 11x + 26y ≤ 130

• 11x + 26y < 130

Aleris is sending a fancy organic fruit basket to her grandma for her birthday. Apples cost RM3 and oranges cost RM2. Aleris can spend no more than RM24 on the gift.

Write an inequality that describes the situation.

Let x = # of apples

Let y = # of oranges

• 3x + 2y < 24

• 3x + 2y ≤ 24

• 3x + 2y > 24

• 3x + 2y ≥ 24

Michael is selling chocolate bars and orange juice in a carnival. Chocolate bars sell for RM2.50 each, and orange juice sell for RM3.50 each. If Michael wants to get more than RM150, write an inequality showing the number of chocolate bars, b, and the number of orange juice, j, he must sell.

• 2.50b + 3.50m > 150

• 2.50b + 3.50m <150

• 2.50m + 3.50b > 150

• 2.50m + 3.50b <1

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