# percentages and ratios

#### uxinox

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

#### Cervesa

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

#### uxinox

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.

#### uxinox

I got no email informing me that Cervesa had answered by post. Is this a bug?

#### topsquark

Forum Staff
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

#### uxinox

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.

topsquark

#### topsquark

Forum Staff
Okay. Please let me know if it happens agian.

-Dan