SOLUTION: Suppose that the sum of two whole numbers is 15, and the sum of their reciprocals is 3/10. Find the numbers.

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Question 433315: Suppose that the sum of two whole numbers is 15, and the sum of their reciprocals is 3/10. Find the numbers.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

x%2By=15
1%2Fx%2B1%2Fy=3%2F10
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x%2By=15......solve for x
x=15-y.....plug in 1%2Fx%2B1%2Fy=3%2F10
1%2F%2815-y%29%2B1%2Fy=3%2F10
%28y%2B15-y%29%2Fy%2815-y%29=3%2F10....cross multiply
150=45y-3y%5E2
3y%5E2-45y%2B150=0........solve quadratic

y=+%28-%28-45%29+%2B-+sqrt%28%28-45%29%5E2-4%2A3%2A150+%29%29%2F%282%2A3%29+
y=+%2845+%2B-+sqrt%282025-1800+%29%29%2F6+
y=+%2845+%2B-+sqrt%28225%29%29%2F6+
y=+%2845+%2B-+15%29%2F6+
y1=+%2845+%2B15%29%29%2F6+

y1=+60%2F6+
y1=+10+

y2=+%2845+-15%29%29%2F6+

y2=+30%2F6+
y2=+5+.....so y=+10+ or y=+5+
now find x

x%2B10=15
x=15-10
x=5.....or

x=15-5
x=10
check:
x=5 and y=10
x%2By=15
5%2B10=15
15=15
their reciprocal:
1%2Fx%2B1%2Fy=3%2F10
1%2F5%2B1%2F10=3%2F10..common denominator
%282%2B1%29%2F10=3%2F10
3%2F10=3%2F10
we will have same result if x=10 and y=5