If a, b, and c are three positive integers and 3a = 8b + 2c, then what

Question

If a, b, and c are three positive integers and 3a = 8b + 2c, then what is the smallest possible value of 5a + b + c ?

A. 4
B. 20
C. 23
D. 32
E. 48

sumitkrocks · Answer

3a = 8b + 2c

a, b and c are positive integers i.e let us minimize a and b to see value of a
3*a = 8+2 =10 not a multiple of 3 not possible ; let us find the nearest value that will fetch an integral value of a i.e 3a = 12 = ( 8 + 4) for b=1 c=2 and a=4

I.e value of 5a + b + c = 5*4+ 1 + 2 =23

(C)  is correct IMO

asishron29181 · Answer

3a = 8b + 2c, smallest possible value of 5a + b + c ?

a = 8b + 2c / 3
a , b and c are positive integers
To find the the least value of 5a + b + c we need to minimize the value of a, as much as possible.

Putting b =1 and c=2
a= 4

5a + b + c = 23

IMO C

IanStewart · Answer

Looking at

3a = 8b + 2c

we can see the right side is even, so 3a must be even, and a must be even. Since everything is a positive integer, 8b is at least 8, and 8b + 2c is greater than 8. So a cannot be 2, because then 3a is too small. So the smallest possible value of a is 4, and if a = 4, then b can only be 1 (because 8b must be less than 12), and c = 2, so 5a + b + c = 23.

That's clearly the minimum, because if we used a larger value of a, then 5a alone would be greater than 23.

kantapong · Answer

Given a,b,c positive intgers, 3a = 8b + 2c, find the smallest values of 5a + b + c

a cannot be 1, 2, 3
a can be 4 => b = 1, c = 2 => 5a + b + c = 23 (C)

KSBGC · Answer

Important note is that all integers are positive . Lowest positive integer is 1. i would like to apply trial and error method to crack this one.

if we see the right hand side , 8b + 2c , sum must be even. Thus , we will only play with even value of 3a meaning a must be even and we have to try to keep it lower as we are looking for smallest value.

Possible values of 3a:

6, 12, 18, 24.....so on

among the values , 12 works .

3a = 12 m a = 4.

if b = 1
c = 2 .

other values can be tried .

5a = 5*4 = 20
b= 1
c=2

20 + 1 + 2 = 23.

the best answer is C.

Showmeyaa · Answer

Given: 3a = 8b + 2c
8b + 2c has to be a multiple of 3
Let's try with a = 1
Not possible as b and c have to be positive integers
a = 2
Not possible as b and c have to be positive integers
a = 3
Not possible as b and c have to be positive integers
a = 4
Yes, a = 4, gives 12 = 8b + 2c or b = 1, c = 2
So, 5a + b + c = 5 * 4 + 1 + 2 = 23, (C) IMO!

HarshaBujji · Answer

IMO C,

Just by picking lowest integer values fro b such tat all are integers.

a,b,c is 4,2,1 So 23

Posted from my mobile device

dcn1102 · Answer

IMO C 23.

Assign 1 to B and 2 to C since the sum should be a multiple of 3.
This means A = 4

bumpbot · Answer

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If a, b, and c are three positive integers and 3a = 8b + 2c, then what

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If a, b, and c are three positive integers and 3a = 8b + 2c, then what

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