Define the system of equations that describes the situation.
Take x as the number of quarters and y as the number of dimes, according to the question the total number of coins, which is the sum of quarter and dimes, is 28:
[tex]x+y=28[/tex]
Also, using the equivalence in cents we know that each quarter is 25 cents and each dime is 10 cents. Expressed as dollars, a quarter equals 0.25 dollars and a dime equals 0.10 dollars. According to the question, the total amount of money is $5.05, this is the sum of the product of 0.25 and the number of quarters and the product of 0.10 and the number of dimes.:
[tex]0.25x+0.10y=5.05[/tex]
Use both equations to define the system of equations:
[tex]\begin{gathered} x+y=28 \\ 0.25x+0.10y=5.05 \end{gathered}[/tex]
Use substitution to solve the system:
[tex]\begin{gathered} x+y=28 \\ y=28-x \end{gathered}[/tex][tex]\begin{gathered} 0.25x+0.1y=5.05 \\ 0.25x+0.1(28-x)=5.05 \\ 0.25x+2.8-0.1x=5.05 \\ 0.15x=5.05-2.8 \\ 0.15x=2.25 \\ x=\frac{2.25}{0.15} \\ x=15 \end{gathered}[/tex]
15 of the coins are quarters.
