Forty-Five

The sum of two numbers is 45. The sum of their quotient and the quotient’s reciprocal is 2.05. What is the product of the two numbers?
Source: mathcontest.olemiss.edu 9/19/2011

SOLUTION
Let x and y be the two numbers.
x+y=45        (1)
\frac{x}{y}+\frac{y}{x}=2.05       
(2)

Simplify Eq. (2)
\frac{x^2+y^2}{xy}=2.05
x^2+y^2=2.05xy        (3)
\left (x+y\right )^2=x^2+2xy+y^2        (4)

Substitute the value of x+y from Eq. (1) and the value of x^2+y^2 from Eq. (3) into Eq. (4)
45^2=2xy+2.05xy
45^2=xy\left (2+2.05\right )
45^2=4.05xy
xy=\frac{45^2}{4.05}
xy=500

Answer: 500

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About mvtrinh

Retired high school math teacher.
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2 Responses to Forty-Five

  1. Mariano,Jimel Ryan D. says:

    There are 7 boxes each written with letter A to G (A for the first box, B for the 2nd and so on). You have 7 balls each with letter A to G (A for the first ball, B for the 2nd and so on) You randomly put one ball in each box (blindfoldedly). Find the probability that you put 3 balls correctly (that is, you put the ball in the box with the same letter)?

    solution here plssss
    this is my email address…. jimelryanmariano@yahoo.com
    thank you

  2. mvtrinh says:

    Sorry for the late response. Please see post “Seven Boxes”.

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