Grade Anc

Grade Anc
Station A, B anc C?

At station A, the ratio of number of women to the number of men on the train was 3:5. At station B, quarter of the men and some women alighted from the train. The ratio of the number of women to the number of men became 8:15. At station C, 100 women and 30 men boarded the train and the ratio of women to men on the train became 1:1.
a) How many passengers were there on the train after station C?
b) How many women alighted at station B?
c) Personal question: For which grade do you think this question should be suited for.

Let Wa be the number of women on the train at station A,
Ma be the number of men on the train at station A,
Wb be the number of women on the train on departure from station B,
Mb be the number of men on the train on departure from station B,
Wc be the final number of women on the train at station C,
and Mc be the final number of men on the train at station C.

Then, in the order that the information is given in the problem,
Wa/Ma = 3/5
Wb < Wa
Mb = Ma − 1/4 Ma
Wb/Mb = 8/15
Wc = Wb + 100
Mc = Mb + 30
Wc/Mc = 1/1

Part a asks for the quantity Wc + Mc.
Part b asks for Wa − Wb
However, this problem is best solved from the back to the front. Because of the indefinite number of women that stepped off the train at station B, solving in terms of the number of women at each station is a less promising approach than solving for the number of women in terms of the number of men.

We can eliminate the variable Wc immediately by noting that
Wc = Mc.
We can then solve for both Wb and Mb in terms of Mc, getting
Wb = Mc − 100
Mb = Mc − 30
The ratio can therefore be rewritten as
(Mc − 100) / (Mc − 30) = 8 / 15,
which may then be multiplied by 15(Mc − 30) may be recast as
15 (Mc − 100) = 8 (Mc − 30)
7Mc = 1260
Mc = 180
At this point, we can answer part a, which is Mc + Wc = Mc + Mc = 360.

We also know that
Wb = 180 − 100 = 80
Mb = 180 − 30 = 150

We may now solve for Ma from the formula
Mb = Ma − 1/4 Ma
= 3/4 Ma
so Ma = 4/3 Mb = 4/3 (150) = 200
Now that we know Ma, we can solve for Wa using the ratio:
Wa = 3/5 Ma = 3/5 (200) = 120

At this point, we may answer part b: the number of women who debark at station B is
Wa − Wb
=120 − 80
= 40

Part c: This question is best as an extra credit or challenge question for a high school class that can solve for an arbitrary number of variables in a set of simultaneous linear equations. Because of the amount of indirection and backward thinking required, it can be expected that only the more capable students would figure out how to attack this problem. Perhaps some of the very best pupils from a class capable of solving linear equations in two unknowns can also figure it out because the equations can be attacked in such a way that only two variables need to be solved at once.

Check out the Grade Anc listings below and save 20% to 70% off retail prices:

 

---

 

Tyler Reed !Video 5! (8th Grade)/Gesu (Phila, PA)/ Class of 2013


 

---

 



 

---

 
SCENARIOS-What next in South Africa public sector strike?
Source: Reuters By Jon Herskovitz JOHANNESBURG, Aug 24 (Reuters) - A strike by more than 1 million South African state workers is set to enter its second week with no apparent resolution for the stoppage that poses ...