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Translate to a system of equations and solve:

1) The sum of two numbers is 36. One number is 2 more than the other. Find the numbers.
Answer: (17,19)

2) Find two numbers whose sum is 66 and whose difference is 18.
Answer: (37,29)

These ones I am not sure of:

3) The difference between two numbers is 16. Three times the larger number is seven times the smaller. What are the numbers?

4) The difference between two numbers is 18. Twice the smaller number plus three times the larger is 74. What are the numbers?

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5 answers

  1. 3) Answer (12, 28)
    4) Answer (4, 22)

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  2. What are the equations for numbers 3 and 4?

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  3. #3: Let the larger be x, the smaller be y

    <The difference between two numbers is 18> ---> x - y = 16
    <Three times the larger number is seven times the smaller> ---> 3x = 7y or 3x-7y = 0

    #4 (same way)
    x - y = 18
    3x + 2y = 74

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  4. um of two numbers is
    43
    and the difference is
    5
    .

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  5. The average of two numbers is equal to twice the positive difference between the two numbers. If the larger number is 35, what is the smaller number.

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