Answer:
The number of quarter coins is 9, the number of dime coins is 5 and the number of nickel coins is 18
Step-by-step explanation:
Let
x ----> the number of quarter coins
y ---> the number of dime coins
z ---> the number of nickel coins
Remember that
[tex]1\ quarter=\$0.25[/tex]
[tex]1\ dime=\$0.10[/tex]
[tex]1\ nickel=\$0.05[/tex]
we know that
[tex]0.25x+0.10y+0.05z=3.65[/tex] ----> equation A
[tex]x=y+4[/tex]
[tex]y=x-4[/tex] ----> equation B
[tex]z=2x[/tex] ----> equation C
Solve the system by substitution
substitute equation B and equation C in equation A
[tex]0.25x+0.10(x-4)+0.05(2x)=3.65[/tex]
solve for x
[tex]0.25x+0.10x-0.40+0.10x=3.65[/tex]
[tex]0.45x=3.65+0.40[/tex]
[tex]0.45x=4.05\\x=9[/tex]
Find the value of y
[tex]y=x-4[/tex]
substitute the value of x
[tex]y=9-4=5[/tex]
Find the value of z
[tex]z=2x[/tex]
[tex]z=2(9)=18[/tex]
therefore
The number of quarter coins is 9, the number of dime coins is 5 and the number of nickel coins is 18
