Question 1147573
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Tutor @ikleyn shows a clever way of solving a problem like this.  Two numbers add to 50 and have a product of 456; so call the two numbers 25+x and 25-x and solve the equation<br>
{{{(25+x)(25-x) = 456}}}<br>
That is a nice shortcut, because the product on the left is 625-x^2, making it relatively easy to solve the problem.<br>
For many students, it will be even faster simply to solve the basic problem by trial and error: find two numbers whose sum is 50 and whose product is 456.<br>
There are many pairs of integers whose sum is 50 and far fewer pairs of integers whose product is 456.  So look for a pair of integers with a product of 456 that has a sum of 50.<br>
456*1  obviously not
228*2
152*3
114*4
76*6
57*8
38*12  AHA!  That's it!