# The total mass of 10 pennies is 27.5 g, which is made up of old and new pennies. Old pennies have a mass of 3 g and new pennies have a mass of 2.5 g. How many old and new pennies are there?Can't figure out equation. Show work?

Aug 6, 2015

You have $5$ new pennies and $5$ old pennies.

#### Explanation:

You know that you have a total of 10 pennies, let's say $x$ old ones and $y$ new ones. This will be your first equation

$x + y = 10$

Now focus on the total mass of the pennies, which is given to be 27.5 g. You don't know how many old and new pennies you have, but you do know what the mass of an individual old penny and of an individual new penny is.

More specifically, you know that each new penny has a mass of 2.5 g and the each old penny has a mass of 3 g. This means that you can write

$3 \cdot x + 2.5 \cdot y = 27.5$

Now you have two equations with two unknowns, $x$ and $y$.

$\left\{\begin{matrix}x + y = 10 \\ 3 x + 2.5 y = 27.5\end{matrix}\right.$

Use the first equation to find write $x$ as a function of $y$

$x + y = 10 \implies x = 10 - y$

Now take this expression into the second equation and solve for $y$

$3 \cdot \left(10 - y\right) + 2.5 y = 27.5$

$30 - 3 y + 2.5 y = 27.5$

$0.5 y = 2.5 \implies y = \frac{2.5}{0.5} = \textcolor{g r e e n}{5}$

This means that $x$ is equal to

$x = 10 - y$

$x = 10 - 5 = \textcolor{g r e e n}{5}$

Therefore, you have $5$ old pennies and $5$ new pennies.