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Jack and Jill have the same number of cards. Jack has sorted his cards into groups of 80 with no leftovers.

Jill has sorte

Question

Jack and Jill have the same number of cards. Jack has sorted his cards into groups of 80 with no leftovers.

Jill has sorted his cards into groups of 75 with no leftovers. They each have less than 2000 cards. How many

cards do they have altogether?

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Mathematics
3 months
2021-07-31T15:28:18+00:00
2021-07-31T15:28:18+00:00 2 Answers
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## Answers ( )

Step-by-step explanation:please mark as best answer and thank me please

Given :Jack and Jill have the same number of cards. Jack has sorted his cards into groups of 80 with no leftovers.Jill has sorted his cards into groups of 75 with no leftovers.

They each have less than 2000 cards.

To Find :How many cards do they have altogether?Solution:Jack and Jill have the same number of cards.

Jack has sorted his cards into groups of 80 with no leftovers.

Jill has sorted his cards into groups of 75 with no leftovers.

Hence Both have card as LCM of 80 and 75 or multiples of LCM of 80 and 75

80 = 2 * 2 * 2 * 2 * 5 = 2⁴ * 5¹

75 = 3 * 5 * 5 = 3¹ * 5²

LCM = 2⁴ * 3¹ * 5²

= 16 * 3 * 25

= 1200

1200 * 2 = 2400

They each have less than 2000 cards.

Hence Each has cards = 1200

Total Cards = 1200 + 1200 = 2400

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