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anonymous

  • 5 years ago

the sum of two numbers is 31. The first is 5 less than the second. Find the numbers.

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  1. shadowfiend
    • 5 years ago
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    Can you convert this into an equation?

  2. anonymous
    • 5 years ago
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    x=5-y ??

  3. shadowfiend
    • 5 years ago
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    Not quite, it's \(x = y - 5\) (making \(y\) 5 less than \(x\)).

  4. shadowfiend
    • 5 years ago
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    So that's the first part, what about the part where it says that `the sum of two numbers is 31'. Can you make that into an equation?

  5. anonymous
    • 5 years ago
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    x+y=31

  6. shadowfiend
    • 5 years ago
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    Right. So now you have two equations: \[\begin{align} x + y &= 31\\ y - 5 &= x \end{align}\]

  7. shadowfiend
    • 5 years ago
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    Can you solve that system of equations?

  8. anonymous
    • 5 years ago
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    y-5+y

  9. anonymous
    • 5 years ago
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    =31

  10. shadowfiend
    • 5 years ago
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    Right, and then can you solve that equation for y?

  11. anonymous
    • 5 years ago
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    that is where i am a little confused. do i minus a y?

  12. anonymous
    • 5 years ago
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    4y?

  13. shadowfiend
    • 5 years ago
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    So you have: y - 5 + y = 31 You can put the ys together: y + y - 5 = 31 Which is the same as: 2y - 5 = 31

  14. anonymous
    • 5 years ago
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    2y=26?

  15. shadowfiend
    • 5 years ago
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    Not quite, remember that if we want to move the 5 over to the right, you have to add 5 to both sides to cancel it on the left: 2y - 5 + 5 = 31 + 5 2y = 36

  16. anonymous
    • 5 years ago
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    oh so i have to add 5 to equal it out since it is negative?

  17. shadowfiend
    • 5 years ago
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    Exactly.

  18. anonymous
    • 5 years ago
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    thats where i went wrong. y=18?

  19. shadowfiend
    • 5 years ago
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    Exactly.

  20. shadowfiend
    • 5 years ago
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    And then what's x?

  21. anonymous
    • 5 years ago
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    x=18-5=13

  22. anonymous
    • 5 years ago
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    13

  23. shadowfiend
    • 5 years ago
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    Exactly!

  24. anonymous
    • 5 years ago
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    thank you. i am going to attempt my next problem.

  25. shadowfiend
    • 5 years ago
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    Cool.

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