Chapter 2 - Section 2.5 - An Introduction to Problem Solving - Exercise Set - Page 165: 14

The number is $4$.

Let $x$ = the unknown number Then "a number increased by 12" means $x+12$ "four times a number" means $4x$ Thus, the equation that represents the situation is: $x+12=4x$ Subtract $x$ on both sides of the equation to obtain: $12=4x-x \\12=3x$ Divide $3$ on both sides of the equation to obtain: $\dfrac{12}{3} = x \\4 = x$