Sue scored a total of 35 points in two games. She scored 6 times as many points in the second game as in the first. How many more points did she score in the second game?
The correct answer and explanation is:
Let’s define variables for the points Sue scored in each game:
- Let xx be the points scored in the first game.
- Since Sue scored 6 times as many points in the second game, the points in the second game are 6x6x.
We know from the problem that the total points scored in both games is 35: x+6x=35x + 6x = 35
Simplify the left side: 7x=357x = 35
Solve for xx: x=357=5x = \frac{35}{7} = 5
So, Sue scored 5 points in the first game.
Next, find points scored in the second game: 6x=6×5=306x = 6 \times 5 = 30
Sue scored 30 points in the second game.
The question asks: How many more points did she score in the second game? This means the difference between second and first game points: 30−5=2530 – 5 = 25
Answer: Sue scored 25 more points in the second game.
Explanation:
This problem is a classic example of using algebra to solve word problems. We start by translating the words into mathematical expressions. Here, “6 times as many points” is translated to multiplying the first game’s points by 6.
By defining the variable xx for the first game’s points, we express the second game’s points as 6x6x, which helps set up the equation reflecting the total points scored over two games.
The total points equation x+6x=35x + 6x = 35 simplifies to 7x=357x = 35. Solving for xx gives the first game’s points, which is 5.
Then, calculating the second game’s points as 6 times that amount yields 30 points.
Finally, subtracting the first game’s points from the second game’s points gives the difference, which is the number of points Sue scored more in the second game compared to the first.
This step-by-step method is fundamental for solving similar problems that involve relationships between quantities and totals. It demonstrates how to translate words into equations, solve for unknowns, and interpret the results in the context of the problem.