Skylar has 40% more pennies than nickels. If the value of Skylar's pennies and nickels is $2.56, how many nickels does Skylar have?

Call the number of nickels, x

Then....the number of pennies is 40%  more  =  1.4x

And the number of each * their denomination each gives us the total value.....so we have...

5x   + 1 (1.4x)    =  256     simplify

5x + 1.4x  = 256

6.4x  = 256       divide both sides by 6.4

x = 40     this is the number of nickels

And 1.4 (40)   = 56      this is the number of pennies

Skylar has 40% more pennies than nickels. If the value of Skylar's pennies and nickels is $2.56, how many nickels does Skylar have?

p = pennies

n = nickels

Skylar has 40% more pennies than nickels:

\(\begin{array}{|rcll|} \hline p &=& n\cdot(1+40\ \%) \\ &=& n\cdot(1+\frac{40}{100}) \\ &=& n\cdot(1+0.4) \\ &=& n\cdot 1.4 \\ \mathbf{p} & \mathbf{=} & \mathbf{1.4\cdot n} \\ \hline \end{array}\)

The value of Skylar's pennies and nickels is $2.56:

\(\begin{array}{|rcll|} \hline p\cdot 1\ \text{Cent} + n \cdot 5\ \text{Cent} &=& 256\ \text{Cent}\\ p + 5\cdot n &=& 256 \qquad & | \qquad p = 1.4\cdot n\\ 1.4\cdot n + 5\cdot n &=& 256 \\ 6.4\cdot n &=& 256 \qquad & | \qquad : 6.4 \\ n &=& \frac{256} {6.4} \\ \mathbf{ n } & {=} & \mathbf{ 40 }\\ \hline \end{array}\)

Skylar does have 40 nickels.

pennies?

\(\begin{array}{|rcll|} \hline p &=& 1.4\cdot n\\ p &=& 1.4\cdot 40\\ \mathbf{ p } & {=} & \mathbf{ 56 }\\ \hline \end{array}\)

and Skylar does have 56 pennies.

Thank you guys!