At the beginning of the contest the jar contains 60 slips for $5, 40 slips for $3, and 50 slips for $x. If the expected value of the first draw from the jar is $5.8, the value of x is .

Question

A bank runs a contest to encourage new customers to open accounts. In the contest, each contestant draws a slip representing a different reward—$5, $3, or $x—from a jar. At the beginning of the contest the jar contains 60 slips for $5, 40 slips for $3, and 50 slips for $x.

If the expected value of the first draw from the jar is $5.8, the value of x is .

At one point in the contest, the jar contains 3 slips for $5, 7 slips for $3, and y slips for $x. If the expected value on the next draw is $6, the value of y is .

Answer 1

(60(5) + 40(3) + 50x)/150 = 5.8

5.8 is a weighted average of 5, 3 and x

x >5

(300+120+ 50x)/150 = 5.8

420 + 50x = 5.8(150)

50x = 870-420 = 450

x = 450/50 = 9 = $9

3(5) + 7(3)) + xy = 6(x). IF x = $9 from the 1st part of the problem

15+21 + 9y = 54

9y = 54-36

y= 18/9 = 2