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30 Mar 2020, 19:14
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C
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Difficulty:
95%
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Question Stats:
47% (02:54) correct
53%
(02:23)
wrong
based on 105
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\(5a+3b+c=17\)
\(a+4b+7c=21\)
Given that a, b and c satisfy the system of equations above, and a+b+c is equal to \(\frac{x}{y}\), where x and y are coprime positive integers, find x+y.
A. 75
B. 90
C. 110
D. 120
E. 135
\(a+4b+7c=21\)
Given that a, b and c satisfy the system of equations above, and a+b+c is equal to \(\frac{x}{y}\), where x and y are coprime positive integers, find x+y.
A. 75
B. 90
C. 110
D. 120
E. 135
Updated on: 31 Mar 2020, 07:59
Originally posted by preetamsaha on 30 Mar 2020, 19:36.
Last edited by preetamsaha on 31 Mar 2020, 07:59, edited 1 time in total.
Last edited by preetamsaha on 31 Mar 2020, 07:59, edited 1 time in total.
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Coefficients of first equation are in A.P with a common difference of (-2).
Coefficients of second equation are also in A.P with a common difference of 3.
Multiplying first equation by the absolute value of the Common difference of the second equation and multiplying second equation by the absolute value of the Common difference of the first equation.
We get,
15a + 9b + 3c = 51
2a + 8b + 14c = 42
Adding both equations we get
17a + 17b + 17c = 93
17(a+b+c)=93
a+b+c= 93/17
So,93 + 17 = 110
correct answer is C
Coefficients of second equation are also in A.P with a common difference of 3.
Multiplying first equation by the absolute value of the Common difference of the second equation and multiplying second equation by the absolute value of the Common difference of the first equation.
We get,
15a + 9b + 3c = 51
2a + 8b + 14c = 42
Adding both equations we get
17a + 17b + 17c = 93
17(a+b+c)=93
a+b+c= 93/17
So,93 + 17 = 110
correct answer is C
General Discussion
30 Mar 2020, 19:55
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preetamsaha
Thanks for the explanation.
How to solve the question, if they were not in AP?
Posted from my mobile device
