Question

A jar contains n nickels and d dimes. There are 18 coins in the jar, and the total value of the coins is $1.15. How many nickels and how many dimes are in the jar? (Hint: Nickels are worth $0.05 and dimes are worth $0.10.)
There are....... nickels and .....dimes in the jar.?

Answer 1

Answer:

There are 13 nickels and 5 dimes in the jar.

Step-by-step explanation:

Total number of coins = 18

Number of nickels =$n$

Number of dimes = $d$

Therefore $n+d=18$

Total value of coins = $1.15

Value of $n$ nickels = $$0.05n$

Values of $d$ dimes = $$0.10d$

therefore $0.05n+0.10d=1.15$

We have a system of equation to solve

(1) $n+d=18$

(2) $0.05n+0.10d=1.15$

Multiplying equation (2) with $-10$

$-0.5n-d=-11.5$

Now adding it to equation (1)

       $n+d=18$

$-0.5n-d=-11.5$

We get $0.5n=6.5$

Dividing both sides by $0.5$

$\frac{0.5n}{0.5}=\frac{6.5}{0.5}$

∴ $n=13$

Plugging value of $n$ in equation (1).

$13+d=18$

Subtracting both sides by 13.

$13+d-13=18-13$

∴ $d=5$

Therefore there are 13 nickels and 5 dimes in the jar.