Answer: (A) Kurt's expression; x = 4.6k
(B) Jared's expression; y = 4.4j
(C) Team's score; z = 4.6k + 4.4j
(D) Team score = 40.6 m
Step-by-step explanation: In order to calculate the average of a given set of data, the formula is to sum up the given data or values and then divide the sum total by the number of values observed. That means, if for instance a student jumps 10 times, his average would be given as the sum of all 10 distances jumped divided by 10. If the sum derived equals 50, then the student's average is 50 divided by 10. In other words;
Average = (∑x)/x
When we cross multiply, this can also result in
Average*x = ∑x
The question has given us the average for both students, hence we can derive their average as described above. If Kurt jumps k number of times, then his average jump will be;
4.6 = (∑k)/k
And remembering that Average*x is the same value as ∑x, we substitute for the value given in the question, which is k. Hence,
4.6*k = ∑k
Note that the total score for each boy can now be determined as the average calculated times the total number of jumps, that is, working backwards. Hence, Kurt's total score is 4.6k.
(a) If we represent Kurt's score as x, then we can express his score as
x = 4.6k ------(1)
(b) If we represent Jared's score as y, then we can express his score as
y = 4.4j ------(2)
(c) The team score is the sum of the scores of both boys. Hence, if the boys scores have been written in terms of x and y then the team score shall be represented by z. Therefore we now have;
z = x + y
z = 4.6k + 4.4j
(d) If Kurt jumps 5 times then his total score will be
x = 4.6k
x = 4.6(5)
x = 23 m
If Jared jumps 4 times then his total score will be
y = 4.4j
y = 4.4(4)
y = 17.6 m
The team score therefore is determined as
z = x + y
z = 23 + 17.6
z = 40.6
The team score is a total of 40.6 m
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