Answer
The person has 5 dimes and 9 quarters.
Work Step by Step
Let's assume that the person has $x$ number of dimes and $y$ number of quarters. As he has $14$ coins in his pocket, Therefore-
$x+y$ = $14$ __eq.1
Now we know that a dime is one tenth of a dollar and quarter is one fourth of a dollar, and the person has $ 2.75$ Dollars in total. Therefore-
$x\times\frac{1}{10}+y\times\frac{1}{4}$ = $2.75$
i.e. $\frac{x}{10}+\frac{y}{4}$ = $2.75$
Multiplying by $20$ on both the sides-
$2x + 5y$ = $55$ __eq.2
Substituting for $x$ in eq.2 from eq.1-
$2(14-y) + 5y$ = $55$
i.e. $28-2y + 5y$ = $55$
i.e. $28+ 3y$ = $55$
i.e. $3y$ = $55-28$ = $27$
i.e. $y$ = $9$
Substituting for $y$ in eq.1-
$x+9$ = $14$
i.e. $x$ = $14-9$ = $5$
Thus the person has 5 dimes and 9 quarters.
