Question 1117140
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The area of a rectangle is length times width.  What two numbers do you know whose difference is 3 and whose product is 28?<br>
7*4 = 28; the table is 7 feet long and 4 feet wide.<br>
Algebra doesn't make the problem any easier....<br>
let x = width
then x+3 = length<br>
The area (length times width) is 28:
{{{x(x+3) = 28}}}
{{{x^2+3x = 28}}}
{{{x^2+3x-28 = 0}}}<br>
To solve that quadratic equation, you need to find two numbers whose difference is 3 and whose product is 28....<br>
But that's what we did in the first place.<br>
Of course it is good to know how to solve problems like this using algebra.  And solving simple examples like this is good practice in setting up problems for solving them algebraically.<br>
But if an algebraic solution is not required, common sense and a little mental arithmetic gets you to the answer much faster.