Respuesta :
Given
He has 34 coins worth $6.10
Let the number of quarters he has be x and the number of dimes hes has be y
He has 34 coins implying:
[tex]x\text{ + y = 34}[/tex]From conversion rates, we have
[tex]\begin{gathered} 4\text{ quarters = 1 dollar} \\ 10\text{ dimes = 1 dollar} \\ 1\text{ quarter = 0.25 dollars} \\ 1\text{ dime = 0.1 dollars} \end{gathered}[/tex]Hence, we can write:
[tex]0.25x\text{ + 0.1y = 6.10}[/tex]To find x and y, we have to solve the equations simultaneously
[tex]\begin{gathered} x\text{ + y = 34} \\ 0.25x\text{ + 0.1y = 6.10} \end{gathered}[/tex]From the first equation:
[tex]\begin{gathered} x\text{ + y = 34} \\ x\text{ = 34 -y} \end{gathered}[/tex]Substituting into the second equation and solving for y:
[tex]\begin{gathered} 0.25(34\text{ -y) + 0.1y = 6.10} \\ 8.5\text{ - 0.25y + 0.1y = 6.10} \\ \text{Collect like terms} \\ -0.15y\text{ = 6.1 - 8.5} \\ -0.15y\text{ = }-2.4 \\ Divide\text{ both sides by -0.15} \\ y\text{ = }16 \end{gathered}[/tex]Substituting to find x:
[tex]\begin{gathered} x\text{ = 34 - y} \\ \text{ = 34 - 16} \\ =\text{ }18 \end{gathered}[/tex]We can conclude that Shana has 18 quarters and 16 dimes
