A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

the second of two numbers is 7 more than the first. their sum is 47. Find the numbers

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    x+y=47, x-y = 7 means that if we add the two questions, 47 + 7 = x + y + x - y = 2x = 54. Then x = 27 and y = 20.

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I am still confused. I am sorry

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok so you're trying to translate this word problem into two equations

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the point being, that two solve a problem with two variables (in this case the two numbers), you need two equations that have both variables in them

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so for the first part of the word problem, it's saying that we have two numbers, and one of the numbers is 7 greater than the other

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    or in other words, y = x + 7, with y being the second number, and x being the first

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    now the second piece of information tells you that when you add both together, they equal 47. so you can write that as an equation like this: x + y = 47

  8. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the next step, once you have as many equations as you do variables to solve for, is to start substituting one into the other

  9. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so in this case, why don't we choose the first equation, that is, y = x + 7, and "substitute" y into the second equation. That is, we can replace all the "y" variables in the second equation (there's only one), with x+7

  10. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so x + y = 47, substituing x + 7 for y, we get x + x + 7 = 40

  11. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    errr sorry, x + (x + 7) = 47

  12. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    if you keep solving this, then we see that 2x + 7 = 47 , 2x = 40, x = 20

  13. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok, so now we KNOW x=20

  14. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and then we substitute it back into either of our equations

  15. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so since x + y = 47, and we know x = 20, we see 20 + y = 47

  16. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and then y = 27

  17. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    does that make more sense?

  18. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok so we had 2x + 7 = 47

  19. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    we need to subtract 7 from both sides

  20. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so 2x = 40

  21. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and now we divide each side by 2

  22. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so x=20

  23. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok. so we sub. 7 to get X by itself?

  24. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    exactly

  25. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the reason we can do that is because we know if you subtract anything from two equal values (e.g. an eqation like 2x+7 = 47), we know that they are STILL equal - since we did the same operation to both values

  26. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i.e. if I have two baskets that have the same number of oranges in them, and I take out two oranges from each, regardless of how many they started with, they still have the same number

  27. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and this property holds true for any operation on equal values (the two sides of an equation)

  28. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    as long as I do the same operation to both sides, I know they're still equal

  29. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    can i post another one? I will try and work on it and see if i get it right?

  30. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok sure

  31. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    do i post here or on the left?

  32. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    on the left =)

  33. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.