Question

find the cost of each.Gwen Chester has $41.70 in her piggybank. She has one more than threetimes as many dimes as she has nick-els, and she has five times as manyquarters as nickels. How many ofeach coin does she have?

Answer 1

Given that

10 dimes = 1 dollar, this is also known as 10 cents.

4 quarters = 1 dollar, this is also known as 25 cents

20 nickels = 1 dollar, this is also known as 5 cents

Let d represent dime

Let q represent quarter

Let n represent nickel

From the first statement,

`d=3n+1`

From the second statement,

`q=5n`

The total of the coins will be,

`d+q+n=\text{ \$41.70}`

Also,

`0.1d+0.25q+0.05n=41.70`

From the first two equations above,

`\begin{gathered} 0.1(3n+1)+0.25(5n)+0.05n=41.70 \\ 0.3n+0.1+1.25n+0.05n=41.70 \\ 0.3n+1.25n+0.05n=41.70-0.1 \\ 1.6n=41.60 \\ (1.6n)/(1.6)=(41.60)/(1.6) \\ n=26 \\ \therefore n=\text{26} \end{gathered}`

Let us now get the quantities of the remaining coins

`\begin{gathered} d=(3n+1)=(3(26)+1)=(78+1)=79 \\ \therefore d=79 \end{gathered}`
`\begin{gathered} q=5n=5(26)=130 \\ \therefore q=130 \end{gathered}`

Hence, the numbers of each coins are

`\begin{gathered} d=79=0.1(79)=\text{ \$7.9} \\ q=130=0.25(130)=\text{ \$32.5}0 \\ n=26=0.05(26)=\text{ \$1.30} \end{gathered}`