Answer:
The first score is 109
Step-by-step explanation:
I am assuming that in the first sentence of the question, you meant:
Sum of the students three scores is 231...
First, let the scores of the first second and third student be a, b and c respectively. We are told that:
a + b + c = 231 . . . . . . . .(1) (sum of students three scores is 231)
a = b + 20 . . . . . . . . . . . (2) (the first is 20 points more than the second)
a + b = 6c . . . . . . . . . . . .(3) (sum of the first two is 6 more times the third)
required, find a.
substituting the value of (a + b) in equation (3) into equation (1), we will have the following:
since a + b = 6c . . . (3)
a + b + c = 231 . . . . . (1), becomes,
(a + b) + c = 231
(6c) + c = 231
7c = 231 (divide both sides by 7)
c = 231 ÷ 7 = 33
∴ c = 33
Next, from equation (2), we know that a = b + 20; this can also be written as:
a - 20 = b
∴ b = a - 20 . . . . . . . (4)
Finally, putting the value of b in equation (4) and the value of c calculated above into equation 1, ( a + b + c = 231), we have the following:
a + (a - 20) + 33 = 231
(a + a) - 20 + 33 = 231
2a + 13 = 231
2a = 231 - 13 = 218
a = 218 ÷ 2 = 109
∴ a = 109
we can also calculate for 'b' by substituting for the value of 'a' in equation 4
b = a - 20 = 109 - 20 = 89.
and to test if the values of a, b and c are correct:
a + b + c = 231
109 + 89 + 33 = 231
denotes the set of elements in both A and C, which is
.
denotes the complement of set B, which is the set of all elements that are in the universal set that are not in set B. In this case, this set is
