I already know the answer... it's 14. However, I do not know how to get this right answer. Please show me step by step. I have a test tomorrow and there will be a question somewhat like this one on it. Thank you so much!!

Question

I already know the answer... it's 14. However, I do not know how to get this right answer. Please show me step by step. I have a test tomorrow and there will be a question somewhat like this one on it. Thank you so much!!

1. A physical education class has three times as many girls as boys. During a class basketball game, the girls average 18 points each, and the class as a whole averages 17 points per person. How many points does each boy score on average?

Answer 1

If the boys average n points each, then just add up the total points

g = 3b
18g + nb = 17(g+b)
54b + nb = 17(3b+b)
54b + nb = 68b
54+n = 68
n = 14

Answer 2

To find the average number of points each boy scores, we can use the information given in the question. Let's break it down step by step:

Step 1: Let's assign variables to the unknown values. Let's say the number of boys in the class is 'b' and the number of girls is 'g.'

Step 2: According to the information given, "a physical education class has three times as many girls as boys." This means the number of girls (g) is three times the number of boys (b). So, we can write an equation: g = 3b

Step 3: In the basketball game, the girls average 18 points each, and the class as a whole averages 17 points per person. Since there are 'g' girls and 'b' boys, the total number of students in the class is (g + b).

Thus, we can write another equation: (g * 18 + b * x) / (g + b) = 17, where 'x' represents the average number of points each boy scores.

Step 4: To solve for 'x,' we need to substitute the value of 'g' from the equation in Step 2. So we have: (3b * 18 + b * x) / (3b + b) = 17

Simplifying the equation, we get: (54b + bx) / 4b = 17

Step 5: Multiplying both sides of the equation by 4b to eliminate the denominator, we get: 54b + bx = 4b * 17

Step 6: Simplifying further, we have: 54b + bx = 68b

Step 7: Next, we subtract 54b from both sides of the equation to isolate 'x': bx = 68b - 54b

Step 8: Further simplifying, we get: bx = 14b

Step 9: Dividing both sides by 'b,' we get: x = 14

Therefore, the average number of points each boy scores is 14.