Question

Together, Katya and Mimi have 480 pennies in their piggy banks. After Katya lost ½ of her pennies and Mimi lost 2/3 of her pennies, they both had an equal number of pennies left. How many pennies did they lose altogether

Answer 1

288 pennies

Further explanation

Given:

• Together, Katya and Mimi have 480 pennies in their piggy banks.
• After Katya lost ½ of her pennies and Mimi lost ²/₃ of her pennies, they both had an equal number of pennies left.

Question:

How many pennies did they lose altogether?

The Process:

Let k = Katya's pennies and m = Mimi's pennies.

Step-1: Finding out the amount of money in the beginning

At first, Katya and Mimi have 480 pennies in their piggy banks.

Equation-1: $\boxed{ \ k + m = 480 \ }$

After Katya lost ½ of her pennies and Mimi lost ²/₃ of her pennies, they both had an equal number of pennies left. That is, the number of pennies remaining from Katya is $\boxed{k - \frac{1}{2}k = \frac{1}{2}k}$, while Mimi is $\boxed{m - \frac{2}{3}m = \frac{1}{3}m}$.

Equation-2: $\boxed{ \ \frac{1}{2}k = \frac{1}{3}m \ }$

From Equation-2, we get $\boxed{ \ k = \frac{2}{3}m \ }$ and substitute into Equation-1.

$\boxed{ \ \frac{2}{3}m + m = 480 \ }$

$\boxed{ \ \frac{2}{3}m + \frac{3}{3}m = 480 \ }$

$\boxed{ \ \frac{5}{3}m = 480 \ }$

$\boxed{ \ m = 480 \times \frac{3}{5} \ } \rightarrow \boxed{\boxed{ \ m = 288 \ }}$

Substitute the value of m into $\boxed{ \ k = \frac{2}{3}m \ }.$

$\boxed{ \ k = \frac{2}{3} \times 288 \ } \rightarrow \boxed{\boxed{ \ k = 192 \ }}$

Therefore, we got Katya's money of 192 pennies and Mimi's money of 288 pennies at first.

Step-2: Finding out how many pennies did they lose altogether

Katya lost ½ of her pennies and Mimi lost ²/₃ of her pennies.

$\boxed{ \ = \Big(\frac{1}{2} \times 192 \Big) + \Big(\frac{2}{3} \times 288 \Big) \ }$

$\boxed{ \ = 96 + 192 \ }$

$\boxed{ \ = 288 \ }$

Thus, they did lose 288 pennies altogether.

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Notes

From $\boxed{ \ k = \frac{2}{3}m \ }$, we can find out their initial money ratio is Katya's: Mimi's = 2: 3.

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Keywords: together, Katya and Mimi, 480 pennies, piggy banks, lost, an equal number, left, lose

Answer 2

Answer:

288 pennies

Step-by-step explanation: