Nathan B. answered • 02/23/18
Tutor
5
(20)
Elementary and Algebraic skilled
The trick to this is that it's a quadratic hidden in a word problem. If we write out the basic problem as it's written, it looks like this:
210 = s + s2
Now, if we subtract 210 from both sides and then order the equation from highest power to lowest, we get the said quadratic:
0 = s2 + s - 210
So we need to break down the problem into its binomials. Since there's no coefficient on the s2 (or more apropos the coefficient is 1), there's only a single s in each:
0 = (s ____ ) (s ____)
Since we have a negative 210, that means that we need one positive and one negative, because we need to multiply to get to -210:
0 = (s + __) (s - __)
The coefficient for the middle term in our quadratic is 1, so since we're subtracting, one term must be 1 larger than the other term for our binary pair. Since 210 ends in a 0, one of the terms is likely either going to end with a 0 or a 5. 20 and 10 are disparate in their multiplications to get to 210, so let's try 15, and see if we can get to -210 with a 14 or 16
(so that 15-14=1, or 16-15=1):
15 * -14 = -210
Awesome. No need to try the -15 and 16 pair, then.
With this new information, our binary pair now looks like this:
0 = (s + 15)(s - 14)
You can FOIL it out to see it returns to our original quadratic. As you can also see, there are two possible solutions for s.
