Respuesta :
Answer:
There are 13 nickels and 5 dimes in the jar.
Step-by-step explanation:
Total number of coins = 18
Number of nickels =[tex]n[/tex]
Number of dimes = [tex]d[/tex]
Therefore [tex]n+d=18[/tex]
Total value of coins = $1.15
Value of [tex]n[/tex] nickels = $[tex]0.05n[/tex]
Values of [tex]d[/tex] dimes = $[tex]0.10d[/tex]
therefore [tex]0.05n+0.10d=1.15[/tex]
We have a system of equation to solve
(1) [tex]n+d=18[/tex]
(2) [tex]0.05n+0.10d=1.15[/tex]
Multiplying equation (2) with [tex]-10[/tex]
[tex]-0.5n-d=-11.5[/tex]
Now adding it to equation (1)
[tex]n+d=18[/tex]
[tex]-0.5n-d=-11.5[/tex]
We get [tex]0.5n=6.5[/tex]
Dividing both sides by [tex]0.5[/tex]
[tex]\frac{0.5n}{0.5}=\frac{6.5}{0.5}[/tex]
∴ [tex]n=13[/tex]
Plugging value of [tex]n[/tex] in equation (1).
[tex]13+d=18[/tex]
Subtracting both sides by 13.
[tex]13+d-13=18-13[/tex]
∴ [tex]d=5[/tex]
Therefore there are 13 nickels and 5 dimes in the jar.
