Emily has 5u game cards. John has 8/13 fewer game cards than Emily. Find the average number of game cards that Emily and John have in all in terms of u.
Emily = 5u
John = (1-8/13)u
To find the average number of game cards that Emily and John have in total, we need to calculate the total number of game cards they have and then divide it by the number of people.
Let's start by finding the number of game cards John has. We are given that John has 8/13 fewer game cards than Emily.
Let's represent the number of game cards Emily has as E.
Therefore, the number of game cards John has is: E - 8/13 * E = E - (8/13)E = (13/13)E - (8/13)E = (13 - 8)/13 * E = 5/13 * E.
Now, let's find the total number of game cards Emily and John have: E + 5/13 * E = (13/13)E + (5/13)E = (13 + 5)/13 * E = 18/13 * E.
Since we are looking for the average number of game cards, we divide the total by the number of people, which in this case is 2.
The average number of game cards is: (18/13 * E) / 2 = (9/13) * E.
Therefore, the average number of game cards that Emily and John have in terms of u is (9/13) * E.
To find the average number of game cards that Emily and John have, we need to know the total number of game cards they have combined and then divide it by 2 (since we are finding the average).
First, let's find the total number of game cards John has by calculating 8/13 fewer game cards than Emily.
John has 8/13 * 5u = (8/13) * 5u = 40u/13 fewer game cards than Emily.
To find the total number of game cards John has, we subtract the number of game cards John has from Emily's total:
Total number of game cards John has = 5u - 40u/13.
Now, let's find the total number of game cards Emily and John have:
Total number of game cards = Emily's game cards + John's game cards
= 5u + (5u - 40u/13).
Simplifying the expression, we get:
Total number of game cards = 5u + 5u - 40u/13
= 10u - 40u/13
= (130u - 40u)/13
= (90u)/13.
Now, we can find the average number of game cards by dividing the total number of game cards by 2:
Average number of game cards = (90u/13)/2
= (90u/13) * (1/2)
= 90u/26
= 45u/13.
Therefore, the average number of game cards that Emily and John have is 45u/13.