Problem Solving Involving Linear Inequalities in Two Variables

Juan was given 20.00 pesos to buy chocolates (x) that cost 3 pesos each, and

candies (y) that cost 2 pesos each. Which of the following correctly represents this

situation?

• 3x + 2y ≥ 20

• 3x + 2y ≤ 20

• 3x + 2y > 20

• 3x + 2y < 20

Based on question #2, if Juan will buy, 5 chocolates, how many cadies (y) can he

possible buy with the remaining money?

• y < 2; less than two candies

• y ≤ 2; at most two candies

• y > 2; more than two candies

• y ≥ 2; at least to candies

The difference in Gab (x) and Liam’s (y) weight is at least 5 kg. Which of the

following correctly represents this situation?

• x - y ≥ 5

• x - y ≤ 5

• x - y > 5

• x - y < 5

If the weight of Liam (y) is 40 kg, what could be the weight of Gab?

• x < 45; Gab is less than 45 kg

• x ≤ 45; Gab is at most 45 kg

• x > 45; Gab is more than 45 kg

• x ≥ 45; Gab is at least 45 kg

Which of the following is the correct representation of “the difference between x

and y is greater than 25?

• x - y < 25

• x - y > 25

• x - y ≤ 25

• x - y ≥ 25

The total amount of your electric (x) and water (y) bill is at most 3000 pesos.

Which of the following correctly represents this situation?

• x + y ≥ 3000

• x + y ≤ 3000

• x + y > 3000

• x + y < 3000

Based on question #2, If your electric bill (x) is 2200 pesos, what could be the cost of your water bill (y)?

• y < 800; The water bill is less than 800 pesos

• y > 800; The water bill is more than 800 pesos

• y ≤ 800; The water bill is at most 800 pesos

• y ≥ 800; The water bill is at least 800 pesos

A jar contains 20 peso bills (x) and 50 peso bills (y). The sum of the money is less than 500 pesos. Which of the following correctly represents this situation?

• 20x + 50y ≥ 500

• 20x + 50y ≤ 500

• 20x + 50y > 500

• 20x + 50y < 500

Based on #4, which of the following is NOT the possible number of twenty-peso bills and fifty-peso bills inside the jar?

• 20 pcs and 2 pcs respectively

• 10 pcs and 5 pcs respectively

• 4 pcs and 8 pcs respectively

• 9 pcs and 6 pcs respective

Which of the following is the correct representation of

“the sum of x and y is at least 10?

• x + y < 10

• x + y > 10

• x + y ≤ 10

• x + y ≥ 10