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?
Step-by-step explanation:
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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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