a simpler ratio question but it got a bit wordy can anyone help?
#simple wordy question
ember nimbus
steady quail
Because they’ve given us the ratio of Y10:Y11 we can figure out how many students from each year were selected. 40 x 5/8=25 selected from Y10 and 40 x 3/8=15 selected from Y11.
The mean for all the students was 7 hours so we can find the total number of hours students said they revised, by reversing the mean process: 40*7=280 hours in total.
The mean for Y11 is 8 hours more than the mean for Y10, we can show this in an expression since we have the total number of students in each branch.
A/15=B/25+8 where A is the total number of hours Year 11s said they studied in a week, and B is the total number of hours Year 10s said they studied in a week.
We know that A+B=280 as we’d worked out earlier (total number of hours for everyone)
A/15 = B/25 + 8
A + B = 280
You can solve these simultaneously to find A and B, and then find the mean for Year 11 (what they’re asking for) which is A/15
Solving simultaneously:
||Rearrange Equation 2: A = 280 - B
Substitute A into equation 1:
(280 - B)/15 = B/25 + 8
(280 - B)/15 - B/25 = 8
(1400 - 5B)/75 - 3B/75 = 8
(1400 - 8B)/75=8
1400 - 8B = 600
800 = 8B
B = 100
Substitute into equation 2 to get A:
A + 100 = 280
A = 180||
Finding the mean for Y11:
||Mean for Y11 is 180/no. of students
180/15=12 hours||
ember nimbus
thanks a lot