The cumulative expense of a group comprising 43 people was 229 cents. If each man spent 10 cents, each woman 5 cents and each child 2 cents, which of the following can be the total contribution made by the women?
(a) 185 cents
(b) 145 cents
(c) 105 cents
(d) 225 cents
(e) 25 cents
(f) 15 cents
Correct Answer: (a), (b), (c), (e)
Explanation:
Let x, y, z be the number of men, women and children respectively.
Then x+y+z = 43 – – – – – -(1)
Then x+y+z = 43 – – – – – -(1)
10x+5y+2z=229 – – — – (2)
Eliminating z we get,
8x+3y=143
The various possibilities for x and y and the total contribution of women in each case are
|
X
|
Y
|
5y
|
|
45
|
1
|
225
|
|
37
|
4
|
185
|
|
29
|
7
|
145
|
|
21
|
10
|
105
|
|
13
|
13
|
65
|
|
5
|
16
|
25
|
However, the first case where X = 45 and Y = 1 is not possible as z would turn out to be negative in this case. (by eqn (1))