Question

20% of the seventh-grade students have math class in the morning. 16 2/3 % of those students also have science class in the morning. If 30 seventh-grade students have math class in the morning but not science class, find how many seventh-grade students there are.

Answer 1

Let's imagine, total number of seventh grade students is x 20% of x= 20x/100 =x/5 16 2/3% of x/5 students also go to science class i.e; 50/3 % of x/5 = x/30 go to science & maths class.......(a) 30 students only goes to maths class( no science) So, x/5-30 students go to science & maths class..........(b) From (a) & (b) we can conclude x/5 - 30 = x/30 Or x/5 - x/30 = 30 or (6x-x)/30 = 30 Or 5x/30 = 30 or 5x = 900 so, x= 900/5 x=180 So, the total number of seventh grade students which we assumed to be x is 180 .

Answer 2

Let x be the number of seventh grade students.

The 20% of the seventh grade students have math class in the morning means mathematically is 20/100.

The 16 2/23% of those students also have science class in the morning means:

16 2/3 & 20/100 = also have class in the morning
83 1/3 * 20/100 = math in the morning but not in science in the morning

30 students have math in the morning but not science in the morning

83 1/3% * 20/100% * x = 30
250/3 * 20/100x = 30
x = 180

There are 180 seventh graders.