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.