percentages and ratios

Oct 2019
4
1
Lincolnshire
Hi everyone,

Having all kinds of problems solving this one!


A group of students are asked how they travel to school.


55\% say they walk to school.


The remaining travel by car or by bus.


The ratio of students who travel by car to those who travel by bus is 2 : 3


140 more students walk than travel by bus.


How many students travel by car?


So, here is my working:


Let the total number of students in the group be n


Let the number who walk be x


Let the number who travel by car be y



Let the number who travel by bus be z



so x + y + z = n .....................(1)



11/20 n = x ............................(2) 55\%



9/20 n = y + z .........................(3) 45\%



and x - z = 140 .......................(4)



combine (2) and (3) and eliminate n



9x - 11y - 11z = 0 ......................(5)



2:3 ratio



2/5 y + 3/5 z = 0.45 n or



2/5 y + 3/5 z = 9/20 n now sub equation 1



2/5 y + 3/5 z = 9/20 (x + y + z)



8y + 12z = 9x + 9y + 9z



9x + y - 3z = 0 .....................(6)



solve (5) and (6) by subtracting



-12y - 8z = 0 so y = -2/3 z ......(7)



sub (4) and (7) into (6)



9(140 + z) -2/3 z - 3z = 0



1260 + 27/3 z - 11/3 z = 0



1260 + 16/3 z = 0 so z = -236.25



and already I feel like I am wrong. I am expecting positive integer results. Is the method wrong or have I made an arithmetic error?



Thanks
 
Dec 2014
153
117
USA
Let the total number of students = x

walkers = 0.55x

0.45x go by car or bus in a ratio of 2:3, which says 0.18x go by car and 0.27x take the bus


0.55x - 140 = 0.27x

Solve for x, then determine 0.18x, the number who travel by car
 
Oct 2019
4
1
Lincolnshire
Let the total number of students = x

walkers = 0.55x

0.45x go by car or bus in a ratio of 2:3, which says 0.18x go by car and 0.27x take the bus


0.55x - 140 = 0.27x

Solve for x, then determine 0.18x, the number who travel by car
I see. I was overcomplicating it! Thanks.
 
Oct 2019
4
1
Lincolnshire
I got no email informing me that Cervesa had answered by post. Is this a bug?
 

topsquark

Forum Staff
Jan 2006
11,575
3,454
Wellsville, NY
I got no email informing me that Cervesa had answered by post. Is this a bug?
Are you referring to post #2? Did you check your preferences to see if anything changed? (We're in the middle of a rather comprehensive upgrade and the site may have resent some settings.)

If there's still a problem then let me know and I'll buck it up the ladder to the Site Ads.

-Dan
 
Oct 2019
4
1
Lincolnshire
Are you referring to post #2? Did you check your preferences to see if anything changed? (We're in the middle of a rather comprehensive upgrade and the site may have resent some settings.)

If there's still a problem then let me know and I'll buck it up the ladder to the Site Ads.

-Dan
Hi Dan,

I am referring to the original post and Cervesa's first reply. I did receive notification of the upgrade when I signed in, so perhaps that's it.
 
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topsquark

Forum Staff
Jan 2006
11,575
3,454
Wellsville, NY
Okay. Please let me know if it happens agian.

-Dan