SOLUTION: Given that S=7a+b+7c and also S=6a+8b+6c, where 51<S<149 and a, b, c and S are integers, find the sum a+b+c. A) 14 B) 15 C) 16 D) 17 E) 18

Question 1187121: Given that S=7a+b+7c and also S=6a+8b+6c, where 51
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

[1]
[2]

Subtract [2] from [1]:

[3]

Substitute [3] in [1]:

We know a, b, and c are integers, so S is an integer. From the last equation, we also know that S is a multiple of 50, and (a+c) is a multiple of 7.

We also know that S is between 51 and 149. The only multiple of 50 between 51 and 149 is 100. So

[4]

Substitute [4] in [3]:

[5]

Combine [4] and [5] to get the answer.

ANSWER: a+b+c = 14+2 = 16 -- answer choice C

RELATED QUESTIONS
Given that S=7a+b+7c and also S=6a+8b+6c, where 51 (answered by greenestamps)
the sum of a,b and c is 14. if 9a + 8b + 6c = 101, what is the value of 2a + b... (answered by tommyt3rd)
Let a quadrilateral be given with sides a, b, c, and d. Suppose the quadrilateral is... (answered by richard1234)
given that A,B,C and D are whole numbers such that A+B=8, B+C=11,B+D=13 and C+D=14, find... (answered by Cromlix,tommyt3rd)
given that A,B,C and D are whole numbers such that A+B=8, B+C=11, B+D=13 and C+D=14, find (answered by tommyt3rd)
s=... (answered by jim_thompson5910)
Given the following sets, select the statement below that is true. A = {r, i, s, k, e,... (answered by MathLover1)
Suppose x⁵y¹⁷=r and x²y⁷=s, If x=r^a/s^b and y=s^c/r^d, find a + b + c +... (answered by CPhill)
If r,s, and t are integers greater than 1, where rs = 15 and st = 33, which of the... (answered by Edwin McCravy)