Respuesta :
Answer:
Number of quarters = 12
Step-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 cents
Therefore value of [tex]d[/tex] dimes = [tex]d\times 10=10d[/tex] cents
Value of 1 quarter = 25 cents
Value of [tex]q[/tex] quarters = [tex]q\times 25= 25q[/tex] cents
Total 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
