Answer:
least common multiple (LCM) of 5 and 12 is 60
F + s = 10
| f - s | = 18
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This means that:
f = 10 - s
And also that:
| f - s | = 18
(f-s)²=18²
f²- 2sf + s² = 324
But f=10-s
So...
(10-s)² - 2s(10-s) + s² = 324
(10-s)(10-s) - 20s + 2s² + s² = 324
100 - 20s + s² - 20s + 2s² + s² = 324
4s² - 40s + 100 = 324
4s² - 40s + 100 - 324 = 0
4s² - 40s - 224 = 0
1/4 * (4s² - 40s - 224) = 1/4 * 0
s² - 10s - 56 = 0
(s-14)(s+4)=0
So s can be either 14 or -4.
When s = 14, f = -4.
When s = -4, f = 14.
I think A but wait for someone else to make sure
