In a basketball game Maria scored 3 times as many points as Holly. In the next game, Maria scored 7 fewer points than she did in the first game, while Holly scored 9 more points than she did in the first game. If they scored the same number of points in the second game, how many points did each score in the first.
Well, let's use our mathematical skills to solve this problem! Let's assume that Holly scored x points in the first game. According to the problem, Maria scored 3 times as many points as Holly, so Maria scored 3x points in the first game.
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.
Let's assume that Holly scored x points in the first game.
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.
Let's denote the number of points Holly scored in the first game as "x." Since Maria scored 3 times as many points as Holly, Maria's score in the first game would be 3x.
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.
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