my P.E. teacher asked the 100 seventh graders in my school if they could swim. Half of the boys and two thirds of the girls said yes. Seventeen boys said no. How many seventh graders know how to swim?
17(2) = 34 amount of boys
100 - 17(2)= 66 amount of girls
1/2 * 34 = 17 boys said yes
2/3 * 66 = 44 girls said yes
44 + 17 = 61 people in total know how to swim
your answer is 61
61
To find the number of seventh graders who know how to swim, we need to calculate the number of boys and girls who know how to swim separately, and then add them together.
Let's start with the boys. We know that half of the boys said yes and seventeen boys said no. So, to find the total number of boys, we can double the number of boys who said no and subtract it from the total number of boys who were asked.
Let's assume the total number of boys is 'B'.
The number of boys who said yes = (1/2)B
The number of boys who said no = 17
Now, we can calculate the total number of boys:
B = (1/2)B + 17
To solve this equation, we can subtract (1/2)B from both sides:
B - (1/2)B = 17
Combining like terms:
(1/2)B = 17
To isolate B, we can multiply both sides of the equation by 2:
B = 17 * 2
B = 34
So, there are 34 boys in the seventh grade.
Now, let's find the number of girls who know how to swim. We know that two-thirds of the girls said yes.
Let's assume the total number of girls is 'G'.
The number of girls who said yes = (2/3)G
Since we don't have any information about the number of girls who said no, we'll leave that as a variable.
Now we can calculate the total number of girls:
G = (2/3)G + X
Next, we'll subtract (2/3)G from both sides:
G - (2/3)G = X
Simplifying the equation, we get:
(1/3)G = X
So, there is one-third of the total number of girls who said no.
Now, let's calculate the number of girls who know how to swim by subtracting the number of girls who said no from the total number of girls who were asked:
Number of girls who know how to swim = G - X
Since X = (1/3)G, we can substitute it in the equation:
Number of girls who know how to swim = G - (1/3)G
To remove the common denominator, we can multiply both terms by 3:
Number of girls who know how to swim = 3G/3 - G/3
Number of girls who know how to swim = (2/3)G
Now, we can substitute the value of G from the previous equation (B = 34) into the equation for the number of girls who know how to swim:
Number of girls who know how to swim = (2/3)G
Number of girls who know how to swim = (2/3)(100 - B)
Number of girls who know how to swim = (2/3)(100 - 34)
Number of girls who know how to swim = (2/3)(66)
Number of girls who know how to swim = 44
So, there are 44 girls in the seventh grade who know how to swim.
To find the total number of seventh graders who know how to swim, we can simply add the number of boys and girls who know how to swim:
Total number of seventh graders who know how to swim = Number of boys who know how to swim + Number of girls who know how to swim
Total number of seventh graders who know how to swim = (1/2)B + (2/3)(100 - B)
Total number of seventh graders who know how to swim = (1/2)(34) + (2/3)(100 - 34)
Total number of seventh graders who know how to swim = 17 + (2/3)(66)
Total number of seventh graders who know how to swim = 17 + (2/3)(66)
Total number of seventh graders who know how to swim = 17 + 44
Total number of seventh graders who know how to swim = 61
Therefore, 61 seventh graders know how to swim.