Please explain to me how to solve this problem:
Reid and Maria both play soccer. This season, Reid scored 4 less than twice the number of goals that Maria scored. The difference in the number of goals they scored was 6. How many goals did each of them score?
maria ---> x goals
Rein ----> 2x-4
2x-4 - x = 6
x = 10
Maria scored 10 and Reid scored 16 goals.
To solve this problem, we can use algebraic equations to represent the relationship between Reid and Maria's goals.
Let's assume that Maria scored x goals. According to the problem, Reid scored 4 less than twice the number of goals that Maria scored. So we can represent Reid's goals as 2x - 4.
The problem also states that the difference in the number of goals they scored was 6. This means that Reid's goals minus Maria's goals equals 6: (2x - 4) - x = 6.
To solve this equation, we can combine like terms:
2x - x - 4 = 6
Simplifying further:
x - 4 = 6
Now, isolate x by adding 4 to both sides of the equation:
x - 4 + 4 = 6 + 4
x = 10
Therefore, Maria scored 10 goals.
To find out how many goals Reid scored, substitute x back into the expression we defined for Reid's goals:
2x - 4 = 2(10) - 4 = 20 - 4 = 16
Therefore, Reid scored 16 goals.
So, Maria scored 10 goals and Reid scored 16 goals.