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Linear Inequalities and Systems of Linear Inequalities in Two Variables 3
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Solve each problem. Choose your answer(s). Note that certain items may have more than one answer.

1. Mr. Ortega would like to invest no more than ₱100,000 of his earnings in two separate investments. The first investment should be at most ₱5000 more than the other. Which of the following are possible amounts of his two types of investments?
₱30,000 and ₱50,000
₱60,000 and ₱40,000
₱50,000 and ₱70,000
₱75,000 and ₱65,000
₱20,000 and ₱100,000
none of the choices
Answer: ₱30,000 and ₱50,000
2. A room has a capacity of 200 people. At least 75 seats are for children and at most 175 seats are for adults. Which of the following are possible values of the number of seats for children and for adults?
75 seats for children and
150 for adults
25 seats for children and
175 for adults
75 seats for children and
175 for adults
50 seats for children and
125 for adults
100 seats for children and
50 for adults
none of the choices
Answer: 100 seats for children and 50 for adults
3. A rectangular garden is to be fenced with a maximum budget of ₱8000. It will cost a minimum of ₱1000 to fence a pair of opposite sides of the garden and a minimum of ₱1500 to fence the other pair of opposite sides. Which of the following are possible values of the costs of fencing for the two pairs of opposite sides?
₱500 and ₱1,500
₱1,000 and ₱1,500
₱2,000 and ₱2,000
₱8,000 and ₱1,500
₱500 and ₱7,500
none of the choices
Answer: ₱2,000 and ₱2,000; ₱1,000 and ₱1,500
4. Jan sells two types of sandwiches during weekends. He sells ham-and-egg sandwiches at P30 each and bacon-and-cheese sandwiches at ₱35 each. He prepares a total of at most 75 sandwiches and targets a total sale of at least ₱2000. Which of the following are possible values of the number of sandwiches of each type?
15 ham-and-egg and
40 bacon-and-cheese sandwiches
20 ham-and-egg and
65 bacon-and-cheese sandwiches
70 ham-and-egg and
15 bacon-and-cheese sandwiches
20 ham-and-egg and
50 bacon-and-cheese sandwiches
50 ham-and-egg and
10 bacon-and-cheese sandwiches
none of the choices
Answer: 20 ham-and-egg and 50 bacon-and-cheese sandwiches
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