Solution-
Hint- A nickel is worth 5 cents and a dime is worth 10 cents.
Suppose x number of nickels and y number of dimes are present.
Worth of nickels = x × 5 =5x cents = [tex]\frac{1}{20}x \ dollar[/tex]
Worth of dimes = y × 10 =10y cents = [tex]\frac{1}{10}y\ dollar[/tex]
Net worth = Worth of nickels + Worth of dimes = $9.45
[tex]\Rightarrow \frac{1}{20}x+\frac{1}{10}y=9.45[/tex]
If the number of dimes is doubled, then
Worth of dimes = 2 × y × 10 =20y cents = [tex]\frac{1}{5}y \ dollar[/tex]
Net worth = Worth of nickels + Worth of dimes = $16.65
[tex]\Rightarrow \frac{1}{20}x+\frac{1}{5}y=16.65[/tex]
Subtracting both the equation,
[tex]\Rightarrow (\frac{1}{20}x+\frac{1}{10}y)-(\frac{1}{20}x+\frac{1}{5}y)=(16.65)-(9.45)=7.2[/tex]
[tex]\Rightarrow \frac{1}{5}y-\frac{1}{10}y=7.2[/tex]
[tex]\Rightarrow \frac{1}{10}y=7.2[/tex]
[tex]\Rightarrow y=72[/tex]
Putting the value of y in any equation will give the value of x,
the value of x was found to be 45.
∴ Number of nickels are 45 and number of dimes are 72.
