Answer :
Answer: Violet has 5 dimes and 15 quarters.
Step-by-step explanation:
let x denotes the number of dimes and y denotes the number of quarters.
Given : Violet has $4.25 worth of dimes and quarters .
Also, 1 dime = $0.1
1 quarter = $0.25
i.e. [tex]0.1x+0.25y=4.25[/tex] (1)
She has 3 times as many quarters as dimes.
i.e [tex]y=3x[/tex] (2)
Substitute the value of y in equation (1) , we get
[tex]0.1x+0.25(3x)=4.25[/tex]
[tex]\Rightarrow\ 0.1x+0.75x=4.25[/tex]
[tex]\Rightarrow\ 0.85x=4.25[/tex]
Divide both sides by 0.85 , we get
[tex]x=5[/tex]
Substitute the value of x in (2) , we get
[tex]y=3(5)=15[/tex]
Hence, Violet has 5 dimes and 15 quarters.