Lena's penny bank is 7/10 full. After she removes 200 pennies, it is 1/2 full. How many pennies can Lena's bank hold?

Question

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Answer 1

Let b stand for bank.

7b/10 - 200 = b/2

 

What we need to do is isolate b. We can start by subtracting b/2 to both sides:

7b/10 - b/2 - 200 = 0

Then we can add 200 to both sides:

7b/10 - b/2 = 200

 

Now we need a common denominator. 10 works as the lowest common denominator (10 goes into 10 one time, and 2 goes into 10 five times).

7b/10 - b/2 * (5/5) = 200

7b/10 - 5b/10 = 200

2b/10 = 200

Simplify:

b/5 = 200

 

Now to finish isolating b, we multiply both sides by 5:

b = 1000

So the bank holds 1000 pennies

 

Let's check:

1000 / 2 = 500 (halfway mark is 500 pennies)

1000 * 7/10 = 700 (7/10 full is 700 pennies)

700 - 200 = 500 (taking out 200 pennies does indeed leave it half-full)