Question

A box holding pennies, nickels and dimes contains thirteen coins with a total value of 83 cents. How many coins of each type are in the box? (These are US coins; a penny is 1 cent, a nickel is 5 cents, and a dime is 10 cents.)

Answer 1

Answer:

The number of pennies,nickels and dimes are (p,n,d)=(3,4,6).

Further explanation:

Given:

A box holding pennies, nickels and dimes contains thirteen coins in a box.

Total value is 83 cents.

Calculation:

Consider p,n and d be the number of pennies, nickel and dimes.

Now, total is 13 coins so $p+n+d=13$

As we know that these following are US coin.

Penny=1 cent

Nickel=5 cents

Dime=10 cents

Step 1:

The value is already given as 83 cents that is 80+3 cents.

80 cents can be possible in many combinations as follows:

(N,D)=(0,8),(2,7),(4,6),(6,5),(8,4),(10,3),(12,2),(14,1),(16,0)

It is given that the total number of cents is 13 so we choose (4,6) as (n,d) .

So the value of nickel n=4

Dimes d=6

Step 2:

The value of p is calculated as follows:

Substitute 4 for n, 6 for d in equation $p+n+d=13$ as follows:

$p+4+6=13$

$p+10=13$

$p=13-10$

p=3

Thus, the number of pennies,nickels and dimes are (p,n,d)=(3,4,6).