Question

Suppose Elizabeth has 50 coins in nickels and dimes only and has a total of $3.15. How many of each coin does she have?

Answer 1

Answer: She has 13 dimes and 37 nickels.

Step-by-step explanation:

We know that

1 dollar = 100 cents

Then, the value of one dime =10 cents =$0.1

and the value of one nickel = 5 cents = $0.05

Given :  Elizabeth has 50 coins in nickels and dimes only and has a total of $3.15.

Let x be the number of dimes and y be the number of nickels , then the required system of equation would be :-

$x+y=50------------------(1)\\\\ 0.1x+0.05y=3.15----------------(2)$

Multiply 10 to eqn (2), we get

$x+0.5y=31.5---------------------(3)$

Subtract eqn (3) from eqn (1), we get

$0.5y=18.5$

Divide both sides by 0.15, we get

$y=\dfrac{18.5}{0.5}=37$

Put value of y in (1), we get

$x+37=50\\\\ x=50-37=13$

Therefore, she has 13 dimes and 37 nickels.