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anonymous

  • 5 years ago

26 fifth graders collected 500 canned goods. If some students collected one more can than the rest, how many collected 19 and how many collected 20?

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  1. anonymous
    • 5 years ago
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    ok, so assuming that the only two options are 19 and 20 cans collected

  2. anonymous
    • 5 years ago
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    right, so the two unknowns are the number of students that collected 19, and the number that collected 20

  3. anonymous
    • 5 years ago
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    so you have two unknowns, and you need two equations to solve

  4. anonymous
    • 5 years ago
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    so we know that: x*19 + y*20 = 500 - with x= te number o students that collected 19, and y being te number of students that collected 20

  5. anonymous
    • 5 years ago
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    we also know that x+y =26 - there are 26 students in all that collected cans

  6. anonymous
    • 5 years ago
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    so our two equations are: 1. x + y = 26 2. 19x + 20y = 500 And now you want to substitute the value of y in the first equation, into the second equation

  7. anonymous
    • 5 years ago
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    so y = 26 - x now replace (subsitute) that in place of the y in the second equation you get: 19 *x + 20(26-x) = 500

  8. anonymous
    • 5 years ago
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    19x + 520 - 20x = 500 -x + 520 = 500 -x = -20 x = 20

  9. anonymous
    • 5 years ago
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    so 20 students got 19 cans

  10. anonymous
    • 5 years ago
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    now subsitute that value back into the first equation: x + y = 26 - given x = 19 19 +y = 26 y = 7

  11. anonymous
    • 5 years ago
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    so 19 students got 19 cans, and 7 got 20 cans

  12. anonymous
    • 5 years ago
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    whoops sorry, 20 got 19 cans, and 6 got 20 cans - not sure where I got the 19 in the previous step

  13. anonymous
    • 5 years ago
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    thank u sandra

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