Answer:
The number of nickels is 45 and the number of dimes is 72.
Step-by-step explanation:
Let
x ----> number of nickels
y ----> number of dimes
Remember that
[tex]1\ nickel=\$0.05[/tex]
[tex]1\ dime=\$0.10[/tex]
so
[tex]0.05x+0.10y=9.45[/tex] ------> equation A
[tex]0.05x+0.10(2y)=16.65[/tex]
[tex]0.05x+0.20y=16.65[/tex] ------> equation B
Solve the system by substitution
we have
[tex]0.05x+0.10y=9.45[/tex] ------> equation A
[tex]0.05x+0.20y=16.65[/tex] ------> equation B
Multiply both equations by 100 both sides
[tex]5x+10y=945[/tex] ---->[tex]5x=945-10y[/tex] --> equation C
[tex]5x+20y=1,665[/tex] ----> equation D
substitute equation C in equation D
[tex](945-10y)+20y=1,665[/tex]
solve for y
[tex]945+10y=1,665[/tex]
[tex]10y=1,665-945[/tex]
[tex]10y=720[/tex]
[tex]y=72\ dimes[/tex]
Find the value of x
[tex]5x=945-10y[/tex]
[tex]5x=945-10(72)[/tex]
[tex]5x=225[/tex]
[tex]x=45\ nickels[/tex]
Alternative Method
Solve the system by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
the solution is the point (45,72)
therefore
The number of nickels is 45 and the number of dimes is 72.
