Question

A collection of nickels and dimes is worth $9.45. If the number of dimes is doubled, the value is $16.65. Find the number of each coin.

Answer 1

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 = $\frac{1}{20}x \ dollar$

Worth of dimes = y × 10 =10y cents = $\frac{1}{10}y\ dollar$

Net worth = Worth of nickels + Worth of dimes = $9.45

$\Rightarrow \frac{1}{20}x+\frac{1}{10}y=9.45$

If the number of dimes is doubled, then

Worth of dimes = 2 × y × 10 =20y cents = $\frac{1}{5}y \ dollar$

Net worth = Worth of nickels + Worth of dimes = $16.65

$\Rightarrow \frac{1}{20}x+\frac{1}{5}y=16.65$

Subtracting both the equation,

$\Rightarrow (\frac{1}{20}x+\frac{1}{10}y)-(\frac{1}{20}x+\frac{1}{5}y)=(16.65)-(9.45)=7.2$

$\Rightarrow \frac{1}{5}y-\frac{1}{10}y=7.2$

$\Rightarrow \frac{1}{10}y=7.2$

$\Rightarrow y=72$

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.

Answer 2

N- nickel
d-dimes

first it is said that we have n+d=9,45
and if we double the dimes we will have
n+2d=16,65

so from the first equation we have n=9,45-d
the second equation then transforms into
n+2d=16,65
9,45-d +2d=16,65
9,45+d=16,65
d= 16,65-9,45
d=7,2

And we get back to the first equation
n+d=9,45
So n=9,45-d
n=9,45-7,2
n=2,25