The sum of the reciprocals of two numbers is 11. Three times the reciprocal of one of the numbers is 3 more than twice the reciprocal of the other number. Find the numbers.
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Let the two numbers be x and y.
#1: 1/x + 1/y = 11
three times the reciprocal of one of the numbers is three more than twice the reciprocal of the other number:
3/x = (2/y) + 3
#2: 3/x - 2/y = 3
Use systems of equations to solve for the numbers. Multiply equation #1 to 3 so we can cancel out 3/x first.
3/x - 2/y = 3
-3/x - 3/y = -33
-5/y = -30
-5 = -30y
y = 1/6
Solve for x using equation #1.
1/x + 1/y = 11
1/x + 6 = 11
1/x = 5
x = 1/5
The numbers are 1/5 and 1/6
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