m1 = 3h1
m2 = m1-7
h2 = h1+9
m2 = h2
now make some substitutions looking for m1 and h1
m1 = 3(h2-9) = 3(m2-9) = 3(m1-7-9)
m1 = 3m1 - 48
2m1 = 48
m1 = 24
so, h1 = 8
check: m2 = 24-7 = 17 = 8+9 = h2
m2 = m1-7
h2 = h1+9
m2 = h2
now make some substitutions looking for m1 and h1
m1 = 3(h2-9) = 3(m2-9) = 3(m1-7-9)
m1 = 3m1 - 48
2m1 = 48
m1 = 24
so, h1 = 8
check: m2 = 24-7 = 17 = 8+9 = h2
Moving on to the second game, Maria scored 7 fewer points than in the first game, so she scored 3x - 7 points. Holly, on the other hand, scored 9 more points than she did in the first game, so she scored x + 9 points.
Now, we're given that they scored the same number of points in the second game. This means that 3x - 7 = x + 9.
To find x, let's solve the equation:
3x - x = 9 + 7
2x = 16
x = 8
So, Holly scored 8 points in the first game, and Maria scored 3 times this amount, which is 3 * 8 = 24 points.
Therefore, Holly scored 8 points in the first game, and Maria scored 24 points.
According to the given information, Maria scored 3 times as many points as Holly. Therefore, she scored 3x points in the first game.
In the next game, Maria scored 7 fewer points than she did in the first game. So, her total score in the second game was (3x - 7) points.
Similarly, Holly scored 9 more points than she did in the first game. So, her total score in the second game was (x + 9) points.
Given that Maria and Holly scored the same number of points in the second game, we can set up the equation:
3x - 7 = x + 9
Let's solve this equation to find the value of x:
3x - x = 9 + 7
2x = 16
x = 8
Therefore, Holly scored 8 points in the first game.
Since Maria scored 3 times as many points as Holly, she scored 3 * 8 = 24 points in the first game.
So, Maria scored 24 points and Holly scored 8 points in the first game.
In the next game, Maria scored 7 fewer points than she did in the first game, so her score in the second game would be (3x - 7). Similarly, Holly scored 9 more points than she did in the first game, so her score in the second game would be (x + 9).
Given that they scored the same number of points in the second game, we can set up an equation: (3x - 7) = (x + 9).
To solve this equation, we can simplify it by combining like terms: 3x - 7 = x + 9.
Next, let's isolate the variables by subtracting x from both sides of the equation: 3x - x - 7 = x - x + 9, which simplifies to 2x - 7 = 9.
To isolate the variable further, we can add 7 to both sides of the equation: 2x - 7 + 7 = 9 + 7, which simplifies to 2x = 16.
Finally, we can solve for x by dividing both sides of the equation by 2: (2x)/2 = 16/2, which gives us x = 8.
Therefore, Holly scored 8 points in the first game, and since Maria scored three times as many points, she scored 3 * 8 = 24 points in the first game.