# Chapter 2 - Section 2.5 - An Introduction to Problem Solving - Exercise Set: 19

$x=50$

#### 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. $3x\div3=150\div3$ $x=50$

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