Question

question 6 of 28 ritas penny bank is \\(\frac{2}{3}\\) full. after she removes 80 pennies, it is \\(\frac{1}{2}\\) full. how many pennies can ritas bank hold?

Explanation:

Step1: Define total capacity

Let $x$ = total pennies the bank holds.

Step2: Set up equation for pennies removed

The difference between $\frac{2}{3}$ full and $\frac{1}{2}$ full is 80 pennies:
$\frac{2}{3}x - \frac{1}{2}x = 80$

Step3: Find common denominator

Convert to sixths to subtract:
$\frac{4}{6}x - \frac{3}{6}x = 80$

Step4: Simplify left side

$\frac{1}{6}x = 80$

Step5: Solve for $x$

Multiply both sides by 6:
$x = 80 \times 6$

Answer:

480