Final answer:
The two numbers in the problem are 1/2 and 2.5. These are found by setting up an equation with the sum of their reciprocals equal to 12/5 and solving for the smaller number x, then multiplying by 5 to find the larger number.
Step-by-step explanation:
Let's denote the smaller number as x and the larger number as 5x (since it is 5 times another). Given that the sum of their reciprocals is 12/5, we can set up an equation as follows:Write the equation for the sum of the reciprocals: 1/x + 1/(5x) = 12/5Find a common denominator and combine the fractions: (5 + 1)/(5x) = 12/5Multiply both sides by 5x to clear the denominator: 6 = 12xDivide both sides by 12 to isolate x: x = 6/12Simplify the fraction: x = 1/2.Since the larger number is 5 times the smaller, we multiply x by 5: 5x = 5(1/2) = 5/2 or 2.5.Therefore, the two numbers are 1/2 and 2.5.
To solve this problem, we can set up two equations based on the given information. Let's assume one number is x and the other number is 5x. The sum of their reciprocals is 12/5, so we can write the equation: 1/x + 1/5x = 12/5.To solve this equation, we can first find a common denominator of 5x. Multiplying the numerator and denominator of the first fraction by 5, we get 5/5x + 1/5x = 12/5. Simplifying, we have 6/5x = 12/Next, we can cross multiply and solve for x: 6 * 5 = 12 * 5x. This gives us 30 = 60x. Dividing both sides by 60, we find x = 1/2.Therefore, one number is 1/2 and the other number is 5 times that, which is 5/2 or 2.5.