Question

Betsy and Marie both got their haircut on the same day bed she gets her haircut every 28 days and Mary gets her haircut every 35 days how many days will it be until they both get their haircut on the same day again

Answer 1

Explanation:

Betsy gets her hair cut every 28 days and Mary gets hers every 35 days"

Find the least common multiple of 28 and 35.

Betsy every 28 days.

Mary every 35 days.

Multiples of 28: {0,28,56,84,112,140,...}

Multiples of 35: {0,35,70,105,140,...}

So the lesser common multiple between 28 and 35 is 140.

or

28 = 2²×7

35 = 5×7

LCM(28, 35) = 2²×5×7

= 140

So

140 days until they both get their haircut on the same day again

Answer 2

140 days until they both get their haircut on the same day again

Explanation:

When two events, A and B, happen every x and y days, respectively, they will happen on the same day in each lcm(x,y) days. lcm(x,y) is the lesser common multiple of x and y which is not 0.

In this question:

Betsy every 28 days.

Mary every 35 days.

Multiples of 28: {0,28,56,84,112,140,...}

Multiples of 35: {0,35,70,105,140,...}

So the lesser common multiple between 28 and 35 is 140.

So

140 days until they both get their haircut on the same day again