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} (1)/(5)th\text{ full} \\ \\ (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:

`(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} (7)/(10)th\text{ full} \\ \\ (7x)/(10)\text{ pennies} \end{gathered}`

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

`(x)/(5)\text{ + 560 = }(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} ((7)/(10)\text{ - }(1)/(5))\cdot x\text{ = 560} \\ \\ (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}`