sandy wrote:
If 0 < n < 100 and 72.42 = k(24 + n/100), then k + n =
Here's another approach:
GIVEN: \(72.42 = k(24 + \frac{n}{100})\)
Expand right side: \(72.42 = 24k+\frac{kn}{100}\)
Multiply both sides by 100 to get: \(7242 = 2400k+kn\)
Factor out the k to get: \(7242 = k(2400+n)\)
ASIDE: Since n is POSITIVE, we know that k is positive.
Since \((3)(2400)=7200\), and since 7200 is pretty close to 7242, let's see how things look if we try factoring a 3 from the left side of the equation.
We get: \(3(2414)= k(2400+n)\)
We can rewrite 2414 as follows: \(3(2400+14)= k(2400+n)\)
At this point, we can see that \(k=3\) and \(n=14\)
So, \(k+n=3+14=17\)
Answer: 17
Cheers,
Brent