Answer:
1,124 pennies.
Step-by-step explanation:
Let x represent the total amount of coins Christine's penny bank can hold.
We know that it is initially 1/5 full. So, the amount of coins in the bank is:
[tex]\frac{1}{5}x[/tex]
We know that she adds 562 pennies in it. So, we will add 562 to our expression:
[tex]\frac{1}{5}x+562[/tex]
And we know that after adding 562 pennies, the bank is now 7/10 full. Therefore:
[tex]\frac{1}{5}x+562=\frac{7}{10}x[/tex]
To find out how many coins the bank can hold, we will simply solve for x.
First, let's multiply both sides by 10 to remove the fractions:
[tex]10(\frac{1}{5}x+562)=10(\frac{7}{10}x)[/tex]
Distribute:
[tex]2x+5620=7x[/tex]
Subtract 2x from both sides:
[tex]5x=5620[/tex]
Divide both sides by 5:
[tex]x=1124[/tex]
Therefore, Christine's penny bank can hold a maximum of 1,124 pennies.
And we're done!
