Question

One-fifth of an even number added to one-sixth of the next even number makes a total of 15. find the two numbers​

(Hint: let the number be x and x + 2.)

Answer 1

To find the two even numbers, we let the first number be x and solved the equation (1/5)x + (1/6)(x + 2) = 15, which resulted in x being 40. Thus, the two even numbers are 40 and 42.

Step-by-step explanation:

To solve the problem where one-fifth of an even number added to one-sixth of the next even number totals 15, let's represent the first even number as x and the next even number as x + 2. According to the given conditions, we can set up the following equation:

\(\frac{x}{5} + \frac{x + 2}{6} = 15\)

To find the value of x, we need to solve this equation:

1. Multiply both sides of the equation by the common denominator, which is 30, to eliminate the fractions:
2. \(6x + 5(x + 2) = 450\)
3. Simplify the equation:
4. \(6x + 5x + 10 = 450\)
5. Combine like terms:
6. \(11x + 10 = 450\)
7. Subtract 10 from both sides:
8. \(11x = 440\)
9. Divide by 11 to solve for x:
10. \(x = 40\)

The first even number is 40, and the next one is 42.

Therefore, the two even numbers are 40 and 42.