Mathematics, 03.07.2019 13:30 laurabwhiddon

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

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Answer from: LuckyCharms988

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.

Learn moreWhat fraction of the entire garden is planted in flowers link Mr. Frye distributed his money equally among his 4 children for their weekly allowance. linkHow much money did Jack keep? link

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

Answer from: Quest

a. is correct

Answer from: Quest

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a) |-1|, |3/2|, |-2|, |-3|, |3.5|

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Together, katya and mimi have 480 pennies in their piggy banks. after katya lost ½ of her pennies an...

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