Question

a b c are non negitive integers such that 28a+30b+31c = 365. a + b + c = ?

Answer 1

Hey there!

I have currently got two logics with the answer! choose which fits the most

The IQ logic :

Normally, if we take a look at the calendar, we have 12 months and sum up all the days we get 365, ( except for the leap year )

28a + 30b + 31c = 365

What does this remind you?

In the calendar, we have months with 28 days, 30 days , 31 days, a, b, c represent the number of months consisting the date

So, in a normal year, we have one month which has 28 days

So, a = 1

We have 4 months having 30 days ( April , June , September , November )

So, b = 4

We have 7 months which have 31 days ( January, March, May, July, August, October and December )

So, c = 7

a , b , c are non-negative

a + b + c = ?

1 + 4 + 7 = ?

a + b + c = 12

yeye! we got it!!

MATHS logic :

28a+30b+31c=365

28a+(28+2)b+(28+3)c=365

28(a+b+c)+(2b+3c)=365

if suppose 2b+3c is zero (suppose)

then 365÷28 is 13.something

then 13×28=364

365-364=1

we cannot get 1 with 2a+3b

so lets try 12

12×28=336

365-336=29

we can get 29 with 2a+3b in this form

2×4+3×7

so b=4 c=7 and we assumed a+b+c=12 so a = 1

put these values in the equation and it satisfies

so the value of a+b+c=12

Hope you get my answer!

The math logic is bit hard to take in ( trail and error method basically )

Hope my answer helps!

#PeaceOut

#FIERCE

Answer 2

yeah sure for your help

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Thanks !

Here is your answer which you are searching for

Well , by simple observation we can tell that this question is refers to a calendar

We know that in a calendar no. of months having 28 days is 1 (i.e. February )

Number of days having 30 days is 4 (i.e. April , June , September , November )

Number of 31 days is 7 ( i.e. January , March , May , July August , October and December)

Now , let's take the above number in place of A , B , C

28 * 1 + 30 * 4 + 31 * 7

A = 1

B = 4

C= 7

A + B + C

1 + 4 + 7 = 12

Hence , the value of a + b +c = 12

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Let us show thar the given answer is 12 only by recast the equation as

28 ( a+ b+c ) + 2b + 3c = 365

If a+b +c > = 13 then 2b + 3c < = 1 which is not possible

Now , recast it again

31 ( a +b + c ) - 3a - b = 365

If a + b + c <= 11 then -3a -b >= 24 , that is not possible

So , a +b +c = 12

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Hope it helpful to you

Be Brainly

Warm Regards

@Brainlestuser