Respuesta :
Answer:
Number of nickels = 19
Number of dimes = 11
Step-by-step explanation:
Given:
Total number of coins =30
Total worth of coins = $2.05
To find the number of nickels and dimes.
Solution:
Let the number of nickels be = [tex]n[/tex]
Let the number of dimes = [tex]d[/tex]
The sum of the coins will be = [tex]n+d[/tex]
The sum equation can be given as :
[tex]n+d=30[/tex].............A
Values of 1 nickel = $0.05
So, value of [tex]n[/tex] nickels in dollars = [tex]0.05n[/tex]
Value of 1 dime = $0.10
So, value of [tex]d[/tex] dimes in dollars = [tex]0.1d[/tex]
The total value of [tex]n[/tex] nickels and [tex]d[/tex] dimes in dollars will be = [tex]0.05n+0.1d[/tex]
Thus, the value equation can be given as:
[tex]0.05n+0.1d=2.05[/tex]..............B
So, the system of equations are:
[tex]n+d=30[/tex].............A
[tex]0.05n+0.1d=2.05[/tex]..............B
Multiplying equation B with -10.
([tex]0.05n+0.1d=2.05[/tex])[tex](\times -10)[/tex]
[tex]-0.5n-1d=-20.5[/tex]
Now, adding to equation A.
[tex]n+d=30[/tex]
[tex]-0.5n-1d=-20.5[/tex]
-----------------------------
[tex]0.5n=9.5[/tex]
Dividing both sides by 0.5.
[tex]\frac{0.5n}{0.5}=\frac{9.5}{0.5}[/tex]
∴ [tex]n=19[/tex]
∴ [tex]d=30-19=11[/tex]
Thus, number of nickels = 19
Number of dimes = 11
