MHB Number of students in a school event

[Johnx1]

During a school event, there were 8 times as many pupils as teachers and there were three times as many boys as girls. There were 70 fewer teachers than boys. How many people were there at the school event?

My answer: is there a better way to do it.

We know that pupils are students

Students = S
boys = B
Teachers = T

So...

S = 8T
Boys = 3G
T = B - 70

Since there is 8x students than teachers, I did Boys = 6x and girls = 2x

I'm going to use this next: S = 8T

8x = 8(B -70)

8x = 8(6x - 70)

8x = 4x - 560

x = 14

We know there is 8x students, so there are 112 students and we know that there is 1/8 of teachers, so there are 14 teachers.

Answer = 126.

 

[HOI]

During a school event, there were 8 times as many pupils as teachers and there were three times as many boys as girls. There were 70 fewer teachers than boys. How many people were there at the school event?

My answer: is there a better way to do it.

We know that pupils are students

Students = S
boys = B
Teachers = T

So...

S = 8T
Boys = 3G
T = B - 70

Very good!

Since there is 8x students than teachers, I did Boys = 6x and girls = 2x

Okay, there were 3 times as many boys as girls and 6= 3*2. the total number of students is 8 x. Why not just use "T" rather than x?

going to use this next: S = 8T

Actually you have already use that when you wrote the total number of students as 8x= 8T.

8x = 8(B -70)

8x = 8(6x - 70)

8x = 4x - 560

? 8 times 6 x is 48x, not 4x!
8x= 48x- 560
40x= 560
x= 560/40= 14 so that "4x" was a typo?

x = 14

We know there is 8x students, so there are 112 students and we know that there is 1/8 of teachers, so there are 14 teachers.

Answer = 126.

Yes, there were 6(14)= 84 boys, 2(14)= 28 girls, and 84- 70= 14 teachers so a total of 84+ 28+ 14= 126 people. Very good!

 

[Johnx1]

Very good! Okay, there were 3 times as many boys as girls and 6= 3*2. the total number of students is 8 x. Why not just use "T" rather than x?Actually you have already use that when you wrote the total number of students as 8x= 8T.

8x = 8(B -70)

8x = 8(6x - 70)

8x = 4x - 560

? 8 times 6 x is 48x, not 4x!
8x= 48x- 560
40x= 560
x= 560/40= 14 so that "4x" was a typo? Yes, there were 6(14)= 84 boys, 2(14)= 28 girls, and 84- 70= 14 teachers so a total of 84+ 28+ 14= 126 people. Very good!

thank you.

Yes, that was a typo :-)---------------------------------
Students = S
boys = B
Teachers = T

So...

S = 8T
Boys = 3G
T = B - 70

I found a different way of doing it.

Since we know T = B -70. And boys = 6T, I did.

T = 6T - 70. Which equals T = 14.

So, S = 8T

S = 8(14) = 112

112 + 14 = 126.Thank you again.