Sara goes to the mall every 6th day. Andy goes to the same shopping mall every 7th day.How many times will they meet in the mall in the month of December and January if we start counting from 1st December.

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08-09-2020
Mathematics

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Sara goes to the mall every 6th day. Andy goes to the same shopping mall every 7th day.How many times will they meet in the mall in the month of December and January if we start counting from 1st December.

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JeanaShupp JeanaShupp · Answer 1 · 2020-09-15T02:52:48+02:00

Answer: Only once.

Step-by-step explanation:

Given: Sara goes to the mall every 6th day. Andy goes to the same shopping mall every 7th day.

Then, from starting the first day , the number of day when they meet = L.C.M of (6,7)

Since 7 is a prime number , so the least common multiple of 6 and 7 = 6 x 7 = 42

So, every 42th day they will meet.

Both December and January have 31 days.

Starting from 1st December , they will meet on 11th January because 42 = 31 +11 , where 31 days are of December and next 11 days of January.

next time they will meet 42 days after Also 20 + 22 , where 20 remaining days of January and 22 of February, so next time they will meet on 22nd February.

So, they will meet only once at 11th January in the month of December and January .

MrRoyal MrRoyal · Answer 2 · 2021-12-03T12:16:57+01:00

Sara and Andy would meet once if counting is started from 1st of December

The number of days in December and January are:

[tex]\mathbf{December = 31}[/tex]

[tex]\mathbf{January = 31}[/tex]

So, the total number of days in both months.

[tex]\mathbf{Total = January + December}[/tex]

So, we have:

[tex]\mathbf{Total = 31 + 31}[/tex]

[tex]\mathbf{Total = 62}[/tex]

Next, we list out the multiples of 6 and 7, up to 62.

The list is as follows:

[tex]\mathbf{6: 6, 12, 24, 30, 36, 42, 48, 54, 60}[/tex]

[tex]\mathbf{7: 7, 14 ,21, 28, 35, 42, 49, 56}[/tex]

The common term between both multiples is

[tex]\mathbf{Common = 42}[/tex]

This means that they would meet 42 days since the beginning of December.

Hence, they would meet just once if counting is started from 1st of December