A, B, C are in a contest. 400 officers are voting to support them and each of
them can only cast one vote. If the ballot shows a result ratio of 2:3 for A and B candidates, 9:5 for B and C candidates, how many tickets had each of A, B and C get? A get________, B get _______ , C get _______.
three calculation:
A + B + C = 400 total tickets
3A- 2B = 0
5B-9C = 0
That
A get 120 tickets
B get 180 tickets
C get 100 tickets
Sorry I don't really understand how u got to the answers. Could you please elaborate, thank you.
How about this approach?
A:B = 2:3 or 6:9
B:C = 9:5 ---> notice the value of B is the same
so A:B:C = 6:9:5 or 6x:9x:5x
6x+9x+5x = 400
20x = 400
x = 20
so A got 6(20) = 120
B got 9(20) = 180
C got 5(20) = 100
Thank you so much for helping me out
To solve this problem, we can set up a system of equations based on the given information.
Let's assume that A, B, and C receive x, y, and z votes respectively.
According to the first ratio, the number of votes for A and B is in a 2:3 ratio. This can be expressed as:
x:y = 2:3
Similarly, according to the second ratio, the number of votes for B and C is in a 9:5 ratio. This can be expressed as:
y:z = 9:5
We also know that the total number of officers voting is 400, so:
x + y + z = 400
To solve this system of equations, we can use substitution or elimination method. Let's use substitution:
From the first ratio x:y = 2:3, we can rewrite it as x = (2/3)y.
Substituting this value of x in the equation x + y + z = 400, we get:
(2/3)y + y + z = 400
Multiplying through by 3 to get rid of the fraction:
2y + 3y + 3z = 1200
5y + 3z = 1200
From the second ratio y:z = 9:5, we can rewrite it as z = (5/9)y.
Substituting this value of z in the equation 5y + 3z = 1200, we get:
5y + 3(5/9)y = 1200
5y + 15/9y = 1200
(45/9)y + (15/9)y = 1200
(60/9)y = 1200
Simplifying:
(20/3)y = 1200
y = (1200 * 3)/20
y = 180
Now that we have the value of y, we can substitute it back into the equations to find the values of x and z.
x = (2/3)y = (2/3) * 180 = 120
z = (5/9)y = (5/9) * 180 = 100
Therefore, A received 120 votes, B received 180 votes, and C received 100 votes.
To summarize:
A gets 120 votes,
B gets 180 votes,
C gets 100 votes.