3x+2y=24

3x = 24 - 2y = 2(12-y)

Since 3x is a multiple of 3, '12-y' or 'y' must be a multiple of 3.

y can take 5 values (0, 3, 6, 9 , 12) and so does x.

B

Let y be the number of Y score i.e., 2 point

3t + 2y = 28
3t = 28 – 2y

28- 2y is an even number.
3t must be an even number.
t must be an even number such that 3t ≤ 28
t can be 0, 2, 4, 6, and 8

There are 5 different possible values of t.

Answer: Option B.

given
3x+2y =24
x = 24-2y/3
x= 2 * ( 12-y)/3
so x can be 0 with y = 12
and value of y =0, 3,6,9,
total 5 values OPTION B

Say 3x: points by X
2y: Points by Y

3x + 2y =24

x = (24-2y)/3
for x to be integer: y can take values: 12, 9, 6, 3, 0

x can take 5 values.

x = 2(12-y)/3

only values for x: 0,
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Solution

Given
In this question, we are given that

• In a certain game,

o A player can accumulate points only by scoring either an X, which counts 3 points, or
o A Y, which counts 2 points

To find
We need to determine

• If a player scored 24 points in the game and t points were made by scoring X's, how many different values could t have

Approach and Working out

• Total points should be of the form 3X + 2Y
• Thus, 3X + 2Y = 24, where X and Y must be ≥ 0
• Possibilities are (X, Y) = (0, 12) or (2, 9) or (4, 6) or (6, 3) or (8, 0)

Thus, option B is the correct answer.

Correct Answer: Option B
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Given: In a certain game, a player can accumulate points only by scoring either an X, which counts 3 points, or a Y, which counts 2 points.

Asked: If a player scored 24 points in the game and t points were made by scoring X's, how many different values could t have?

Let x be the times X was scored and y be the times Y was scored

t = 3x

3x + 2y = 24

(x,y) = {(0,12),(2,9),(4,6),(6,3),(8,0)}: 5 set of values

t will have 5 different values.

IMO B
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So, if X's are worth 3 points and Y's are worth 2 points, then the TOTAL points = 3X + 2Y (where X and Y represent the number of X's and Y's scored, respectively)
So, we want to determine the number of different integer solutions to 3X + 2Y = 24
Let's list them in the form (X, Y):
(0, 12)
(2, 9)
(4, 6)
(6, 3)
(8, 0)

So, X can equal 0, 2, 4, 6, or 8, then t can equal 0, 6, 12, 18 or 24

Answer: B
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