FIND THE ANSWERS

A+b+c+d=21, c+a+a+b=18, d+a+a+b=19, c+b+c+d=23, a+c+c+d=19, b+b+a+a=20, and d+d+a+b=22, what is a, b, c and d?

Answer this question

  • A+b+c+d=21, c+a+a+b=18, d+a+a+b=19, c+b+c+d=23, a+c+c+d=19, b+b+a+a=20, and d+d+a+b=22, what is a, b, c and d?


Answers

Answer #1 | 09/06 2015 17:53
From the first 2 equations: a = d - 3 (21 - 18 = 3) From the second and third equation: c = d - 1 From the 4th and 5th equations: a = b - 4 Solution 1: From b + b + a + a = 20: 2a + 2b = 20 ; b = a + 4 2a + 2(a + 4) = 20 <=> 2a + 2a + 8 = 20 <=> 4a = 12 a = 12 / 4 = 3 You can already solve it from here, but there is another way to do it(Refer to end). ---------------- a = 3 b = a + 4 = 7 c = d - 1 = 5 d = a + 3 = 6 ---------------- Solution 2: From the last 2 equations: a + b = 2d - 2 b = 2d - 2 - a = 2d - 2 - (d - 3) = 2d - 2 - d + 3 = d + 1 a + b + c + d = d - 3 + d + 1 + d - 1 + d = 21 4d - 3 = 21 <=> 4d = 24 d = 6 ---------------- a = d - 3 = 3 b = d + 1 = 7 c = d - 1 = 5 d = 6 ----------------
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Answer #3 | 09/06 2015 18:26
b+b+a+a=20 2b+2a=20 b+a=10 c+b+c+d=23 a+c+c+d=19 subtract b-a=4 b+a=10 b-a=4 add 2b=14 b=7 therefore a=3 c+b+c+d=23 A+b+c+d=21 subtract c-a =2 c-3=2 therefore c=5 A+b+c+d=21 3+7+4+d=21 therefore d = 6 a=3, b=7, c=5, d=6
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Answer #5 | 10/06 2015 00:53
From the first 2 equations: a = d - 3 (21 - 18 = 3) From the second and third equation: c = d - 1 From the 4th and 5th equations: a = b - 4 Solution 1: From b + b + a + a = 20: 2a + 2b = 20 ; b = a + 4 2a + 2(a + 4) = 20 <=> 2a + 2a + 8 = 20 <=> 4a = 12 a = 12 / 4 = 3 You can already solve it from here, but there is another way to do it(Refer to end). ---------------- a = 3 b = a + 4 = 7 c = d - 1 = 5 d = a + 3 = 6 ---------------- Solution 2: From the last 2 equations: a + b = 2d - 2 b = 2d - 2 - a = 2d - 2 - (d - 3) = 2d - 2 - d + 3 = d + 1 a + b + c + d = d - 3 + d + 1 + d - 1 + d = 21 4d - 3 = 21 <=> 4d = 24 d = 6 ---------------- a = d - 3 = 3 b = d + 1 = 7 c = d - 1 = 5 d = 6 ----------------
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Answer #8 | 10/06 2015 01:26
b+b+a+a=20 2b+2a=20 b+a=10 c+b+c+d=23 a+c+c+d=19 subtract b-a=4 b+a=10 b-a=4 add 2b=14 b=7 therefore a=3 c+b+c+d=23 A+b+c+d=21 subtract c-a =2 c-3=2 therefore c=5 A+b+c+d=21 3+7+4+d=21 therefore d = 6 a=3, b=7, c=5, d=6
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