Question

Together, katya and mimi have 480 pennies in their piggy banks. after katya loses 1 2 of her pennies and mimi loses 2 3 of her pennies, they have an equal number of pennies left. how many pennies did they lose altogether?

Answer 1

Katya and Mimi initially had 192 and 288 pennies respectively. They both lost 96 pennies, so they lost a total of 192 pennies altogether.

Step-by-step explanation:

To solve this problem, we'll start by setting up an equation based on the given information. Let's say that Katya has x pennies, so Mimi has 480 - x pennies. After Katya loses 1/2 of her pennies, she is left with 1/2x pennies. After Mimi loses 2/3 of her pennies, she is left with 1/3(480 - x) pennies. Since they have an equal number of pennies left, we can set up the equation:

1/2x = 1/3(480 - x)

To solve for x, we'll first distribute 1/3:

1/2x = 160 - 1/3x

Next, we'll combine like terms:

1/2x + 1/3x = 160

Using a common denominator of 6, we can add the fractions:

3/6x + 2/6x = 160

5/6x = 160

To isolate x, we'll multiply both sides by the reciprocal of 5/6, which is 6/5:

x = (160)(6/5) = 192

So Katya initially had 192 pennies and Mimi initially had 480 - 192 = 288 pennies. To find out how many pennies they lost altogether, we'll subtract the number of pennies they have left from their initial amounts:

Katya lost 192 - 1/2(192) = 192 - 96 = 96 pennies

Mimi lost 288 - 2/3(288) = 288 - 192 = 96 pennies

Therefore, they lost a total of 96 + 96 = 192 pennies altogether.