# algebra 1 - reciprocals

One number is 3 times another. If the difference of the reciprocals of the two numbers is 12 find the numbers

### Comments for algebra 1 - reciprocals

 Mar 16, 2011 Algebra 1 - Reciprocals by: Staff The question: One number is 3 times another. If the difference of the reciprocals of the two numbers is 12 find the numbersThe answer:One number is 3 times another. If the difference of the reciprocals of the two numbers is 12 find the numbersI?m going to make a point of the definitions because there are actually two sets of solutions, depending on which number is first and which number is second.x = 1st number (called "one number" in the problem description)y = 2nd number (called "another number" in the problem description)One number is 3 times another.x = 3*yIf the difference of the reciprocals of the two numbers is 12 find the numbers. The reciprocal of x is 1/x.The reciprocal of y is 1/y.The problem does not state whether 1/x - 1/y = 12, or 1/y - 1/x = 12. The answer will be different, depending on which equation is used. I'm going to assume the following is true because that is the order the numbers are presented in the statement of the problem: 1/x - 1/y = 12There are now two equations with two unknowns:x = 3*y1/x - 1/y = 12First, solve for y.To solve for y, substitute 3*y for x in the second equation.1/(3*y) - 1/y = 12Multiply each side of the equation by yy*[1/(3*y) - 1/y] = y*12y*1/(3*y) - y*1/y = 12y(1/3)*(y/y) - 1*(y/y) = 12y(1/3)*1 - 1*1 = 12y(1/3) - 1 = 12y-(2/3) = 12yDivide each side of the equation by 12-(2/3)/12 = 12y/12-(2/3)/12 = y*(12/12)-(2/3)*(1/12) = y*1-(2/3)*(1/12) = y-(2*1)/(3*12) = y-2/36 = y-1/18 = ySolve for x by substituting -1/18 for y in the first equation.x = 3yx = 3(-1/18)x = -3/18x = -1/6The final answer is: x = -1/6, y = -1/18Both answers are negative. However, if . . . . . . . . . you use 1/y - 1/x = 12 for the second equation, the answers will be positive:x = 1/6 and y = 1/18Thanks for writing.Staff www.solving-math-problems.com