Write a system of two equations that can be used to answer this question. A sum of money amounting to $3.70 consists of dimes and quarters. If there are 19 coins in all, how many are quarters?

Answer: Number of quarters = 12Step-by-step explanation:Let number of dimes  be = [tex]d[/tex]Let number of quarters be = [tex]q[/tex]Total number  of coins =19 Therefor the first equation would be :[tex]d+q=19[/tex]Total sum of money = $3.70 = [tex]3.70\times100 \ cents= 370 \ cents[/tex]Value of 1 dime = 10 centsTherefore value of [tex]d[/tex] dimes = [tex]d\times 10=10d[/tex] centsValue of 1 quarter = 25 centsValue of [tex]q[/tex] quarters = [tex]q\times 25= 25q[/tex] centsTotal value of coins =[tex]10d+25q[/tex]Therefore the 2nd equation would be:[tex]10d+25q=370[/tex]So the system can be written as :[tex]d+q=19\\10d+25q=370[/tex]We can solve the system using substitution method:Taking equation 1[tex]d+q=19\\[/tex]Subtracting both sides by [tex]q[/tex][tex]d+q-q=19-q\\d=19-q[/tex]Substitution the value of [tex]d[/tex] in equation 2.[tex]10(19-q)+25q=370[/tex]Now, we need to solve for [tex]q[/tex]Using distribution.[tex](10\times 19)-(10\times q)+25 q=370\\190-10q+25q=370\\[/tex]Combining like terms.[tex]190+15q=370[/tex]Subtracting both sides by 190.[tex]190-190+15q=370-190\\15q=180[/tex]Dividing both sides by 15.[tex]\frac{15}{15}q=\frac{180}{15}\\\\q=12[/tex]Therefore number of quarters = 12