Question

9. A school long-jump

team is competing
at the Aberfoyle
international track
meet. Kurt jumps
an average of 4.6 m,
and Jared jumps an
average of 4.4 m.
Each boy's score
is the sum of the
lengths of his jumps.
The team score is
the sum of the
scores of both boys.

a) Write an algebraic expression that
represents Kurt's score if he jumps
k times.

b) Write an algebraic expression that
represents Jared's score if he jumps
j times.

c) Use your results in parts (a) and (b) to
write an algebraic expression for the
team score.

d) Evaluate your expression in part (c) to
determine the team score if Kurt jumps
5 times and Jared jumps 4 times.


Can anyone help me I don't get it

Answer 1

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