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Systems of Linear Equations and Inequalities in Two Variables 1
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Solve each problem. Choose your answer(s). Note that certain items may have more than one answer.

1. If Maritz gives ₱3 to Jonas, she and Jonas will have the same amount of money. If he gives ₱3 to Maritz, she will have 4 times the amount of money he will have. How much did each of them have originally?
Maritz has ₱13 and Jonas has ₱7.
Maritz has ₱16 and Jonas has ₱4.
Maritz has ₱12 and Jonas has ₱8.
none of the choices
Answer: Maritz has ₱13 and Jonas has ₱7.
2. Working together, it takes Leah and Sonia 3 3 4 h to type a manuscript for their history project. Moreover, they can finish typing the same manuscript if Leah types for 3 h and Sonia for 5 h. How long will it take each of them to type the entire manuscript alone?
It will take Leah 6 h and it will take Sonia 10 h.
It will take Leah 8 h and it will take Sonia 12 h.
It will take Leah 8 h and it will take Sonia 10 h.
none of the choices
Answer: It will take Leah 6 h and it will take Sonia 10 h.
3. The sum of two numbers is no more than 13. The second number is at most twice the first number. Which of the following are possible values of the numbers?
−1 and −4
2 and 6
−2 and 4
12 and −6
9 and 3
none of the choices
Answer: −1 and −4; 12 and −6
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