Question

Christine's penny bank is 1/5 full after she adds 560 pennies it is 7/10 full how many pennies can her bank hold?

Answer 1

We will assign a variable to the total capacity of Christine's penny bank to hold pennies as:

$x\colon\text{ Total capacity}$

The bank was initally full to some extent expressed as a fraction of the total capacity of the penny bank as follows:

$\begin{gathered} \frac{1}{5}th\text{ full} \\ \\ \frac{x}{5}\text{ pennies in the bank} \end{gathered}$

She then adds a certain number of pennies in the bank as follows:

$560\text{ pennies added to the bank}$

The total capacity of the bank utilized/filled with pennies can be expressed as a sum of inital capacity and the number of pennies Christine added as follows:

$\frac{x}{5}\text{ + 560}$

Christine find that after adding 560 pennies to the bank it was filled to a new fraction of the total capacity as follows:

$\begin{gathered} \frac{7}{10}th\text{ full} \\ \\ \frac{7x}{10}\text{ pennies} \end{gathered}$

We can equate the expression for number of pennies in the bank to the fraction above as follows:

$\frac{x}{5}\text{ + 560 = }\frac{7}{10}\cdot x$

We have an equation with one variable ( x ). We can solve the above equation by algebraic manipulation as follows:

$\begin{gathered} (\frac{7}{10}\text{ - }\frac{1}{5})\cdot x\text{ = 560} \\ \\ \frac{1}{2}\cdot x\text{ = 560} \\ \\ x\text{ = 1,020 pennies} \end{gathered}$

Hence, the total number of pennies that Christine's bank can withold is:

$1,020\text{ pennies}$