Question 1130918
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If you try to solve this problem using formal algebra, you end up having to solve the quadratic equation<br>
{{{8x^2+10x-7500 = 0}}}<br>
Of course you can always solve a quadratic equation using the quadratic formula.  But if you try to solve by factoring, there is a lot of trial and error in the process.<br>
The problem is solved far more easily (if a formal algebraic solution is not required!) by doing the trial and error with the given information: find two numbers whose product is 7500 that satisfy the condition that one number is 10 more than 8 times the other.<br>
We don't need to do blind guessing; we can make some useful approximations.<br>
We can make the approximation that the longer side is 8 times the shorter side instead of 10m more than 8 times as long.<br>
Then the approximate equation is 8x^2=7500, and we can approximate that with 8x^2=8000, or x^2=1000.<br>
Then we can see that x should be a number close to 30.<br>
And 30 times 250 is 7500; and 250 is 10 more than 8 times 30.<br>
If your mental arithmetic is good, solving the problem like that is much less work than using formal algebra.