#### Answer

$x=50$

#### Work Step by Step

Let x = the unknown number
Then
"the quotient of three times a number and 5" means $3x\div5$ or $\frac{3x}{5}$
"is increased by 4" means to add 4 to the quotient
Thus, the equation that represents the situation is:
$\frac{3x}{5}+4=34$
Use the addition property of equality to subtract 4 from both sides of the equation.
$\frac{3x}{5}+4-4=34-4$
$\frac{3x}{5}=30$
Use the multiplication property of equality to multiply both sides of the equation by 5.
$\frac{3x}{5}\times5=30\times5$
$3x=150$
Use the multiplication property of equality to divide both sides of the equation by 3.
$3x\div3=150\div3$
$x=50$