Daryl has a coin jar containing nickels quarters and one dol

Daryl has a coin jar containing nickels, quarters, and one dollar coins. He has a total of 44 coins totaling $9.75. And, he has five times as many nickels as he has one dollar coins. How many of each coin denomination does he have? Show all work.

Write a system of equations that can be used to solve this problem. Explicitly de- fine what your variables represent. Do not solve your system of equations.

(HINT: A nickel is worth $0.05 and a quarter is worth $0.25)

Solution

Answer:

Daryl has a coin jar containing nickels, quarters, and one dollar coins.

Let N be the number of nickles ,Q be the number of quarters and D denote .the number of dollars

Since he has a total of 44 coins .

So that we have N+Q+D=44

since he has five times as many nickels as he has one dollar coins, so that N=5D

So we have 5D+Q+D=44 => 6D+Q=44

The ratio of nickle , quarter and dollar is 1 : 1/4 : 1/20 or 20: 4 :1 (Value)

Since one nickle is equal to $0.05 and one quarter is equal to $0.25

The totaling of amount is $9.75.

for D=5, then N=5xD=25 and Q=14

Cleary he has N+Q+R=25+14+5=44 coins

and the value of the sum of the coins is 25x0.05+14x0.25+5x1=9.75$

Hence