I Need help with the following question:
If moe has 3x as many singles as larry, and Larry has 4X as many doubles as curly. How many singles and doubles did they each have. They only got singles and doubles. They all had the same number of singles and doubles and the total hits for all 3 was under 200
Since you know that they all had the same number of singles and doubles, you have only three unknowns to solve for. Let x be the number of singles (and doubles) for Mo, y be that number for Larry, and z be that number for Curly
x = 3y
y = 4z
2x + 2y + 2z < 200
6y + 2y + y/2 < 200
8.5 y < 200
y<23
x, y, and z must be integers. See what combinations will work.
205
To solve this problem, we can break it down step by step.
Let's assume that Larry has "x" doubles. According to the given information, Larry has 4 times as many doubles as Curly. Therefore, Curly must have "x/4" doubles.
Now, it is stated that Moe has 3 times as many singles as Larry. So, if Larry has "y" singles, then Moe must have "3y" singles.
Since the total number of hits for all three players is under 200, we can set up an equation:
x + (x/4) + y + (3y) < 200
Simplifying this equation, we can combine like terms:
(9/4)x + 4y < 200
Now, let's consider what values of "x" and "y" make this equation true while also fitting the given conditions.
Since the number of doubles cannot be a fraction, let's test different values of "x" to see if it satisfies the equation.
When x = 1, the equation becomes (9/4) + 4y < 200, but this is not possible since the left side is less than 2.
When x = 2, the equation becomes (9/2) + 4y < 200, but this is still not possible.
When x = 3, the equation becomes (27/4) + 4y < 200, which is still not possible.
Continuing this process, we find that x = 4 is the smallest whole number that satisfies the equation.
So, Larry has 4 doubles. Since Larry has 4 times as many doubles as Curly, Curly must have 1 double (4/4 = 1).
Now, let's solve for "y" in the equation:
(9/4)(4) + 4y < 200
9 + 4y < 200
4y < 191
y < 47.75
Since we are dealing with whole numbers, we need to find the largest whole number less than 47.75. Therefore, y = 47.
So, Larry has 4 doubles and 47 singles, Curly has 1 double and 47 singles, and Moe has 3 times as many singles as Larry, which is 3*47 = 141 singles.
Therefore, Larry has 4 doubles and 47 singles, Curly has 1 double and 47 singles, and Moe has 141 singles.