Chapter 0, Problem 57PR

To determine

To find: The greater number from the two consecutive even integers in the given condition.

Answer to Problem 57PR

The greater number is 4.

Explanation of Solution

Given:

Five times the greater of two consecutive even integers is 14 greater than three times the lesser number.

Calculation:

Consider the two consecutive even integers are $x$ and $x+2$ .

According to the given condition, that is, five times the greater of two consecutive even integers is 14 greater than three times the lesser number,

  $5\left(x+2\right)=14+3x$

Solve the equation $5\left(x+2\right)=14+3x$ as,

  $\begin{array}{c}5\left(x+2\right)=14+3x\\ 5x+10=14+3x\\ 5x-3x=14-10\\ 2x=4\\ x=2\end{array}$

Therefore, the two consecutive even integers are 2 and 4.

Thus, the greater number is 4.