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Mathematics

Grade10

Easy

Question

The sum of two numbers is 18, and the product of these two numbers is 56. What are the numbers?

4 and 14
10 and 8
8 and 7
2 and 28

The correct answer is: 4 and 14

First, we know two things:
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell text smaller end text left parenthesis S right parenthesis plus text larger end text left parenthesis L right parenthesis equals 18 not stretchy rightwards double arrow L equals 18 minus S end cell row cell S cross times L equals 56 end cell end table$
Substituting $18 minus S text for end text L$ in the second equation gives:
$S left parenthesis 18 minus S right parenthesis equals 56$
Multiplying this out gives:
$18 S minus S squared equals 56$
Which rearranges to:
$S squared minus 18 S plus 56 equals 0$
Second, factor this quadratic to get our solution:
$table attributes columnalign right columnspacing 1em end attributes row cell S squared minus 18 S plus 56 equals 0 end cell row cell left parenthesis S minus 4 right parenthesis left parenthesis S minus 14 right parenthesis equals 0 end cell row cell S equals 4.14 end cell end table$
Therefore:
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell S equals 4 comma L equals 18 minus 4 equals 14 end cell row cell S equals 14 comma L equals 18 minus 14 equals 4 text (this solution is rejected) end text end cell end table$

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