Question

Carolyn has $3.25 in her purse in nickels and dimes. The number of nickels is five less than three times the number of dimes. Find the number of each type of coin

Answer 1

Let x be the number of nickels and y be the number of dimes in Carolyn's purse.

There is $3.25 in her purse in nickes and dimes. T

Recall that;

`\begin{gathered} 1\text{ dime}=\text{ \$}0.1 \\ \\ 1\text{ nickel }=\text{ \$}0.05 \end{gathered}`

Thus;

`0.05x+0.1y=3.25..........equation1`

Also, the number of nickels is five less than three times the number of dimes. Thus;

`x=3y-5...........equation2`

Substitute equation2 in equation1;

`\begin{gathered} 0.05(3y-5)+0.1y=3.25 \\ \\ 0.15y-0.25+0.1y=3.25 \\ \\ 0.25y=3.25+0.25 \\ \\ y=(3.5)/(0.25) \\ \\ y=14 \end{gathered}`

Substitute the value of y in equation2;

`\begin{gathered} x=3(14)-5 \\ \\ x=37 \end{gathered}`

Hence, there are 37 nickels and 14 dimes in Carolyn's purse.