Finding the Maximum Seats of Two Vans Using Linear Algebra

[yuuri14]

Homework Statement

A co. use two vans 7-9am. 1 van has 5 more seat than the other. The smaller van makes two trips, larger 1 trip?
The maximum seats of both vans that was given would be 71.
Let x be the seats of small van and y be the seat of the larger van.
How many seats does the larger van have?

PLEASE HELP! I know that I have to use a linear function hear. PLEASE GIVE AN EQUATION TO THIS PROBLEM. THANK YOU!

Homework Equations

well i know that I only can use the given information.
here what I got so far:
y= x+5... because it has 5 more seats than the smaller van, which has x seats.
PLEASE HELP!

 

[CompuChip]

Yes, the equation you gave is correct.
There is one other equation hidden in the text. More precisely, in this line:

The maximum seats of both vans that was given would be 71.

 

[yuuri14]

Yes, the equation you gave is correct.
There is one other equation hidden in the text. More precisely, in this line:

would it be x+y=71 because x=the smaller van and y= the larger van...put them together it has a seat of 71

AND if that's the case what's after this
y=x+5
71=x+y

 

[mg0stisha]

you can take the first equation and substitute it into the second equation, leaving a new equation with only one variable, which you can then solve for.

 

[yuuri14]

you can take the first equation and substitute it into the second equation, leaving a new equation with only one variable, which you can then solve for.

y=x+5
71=x+y
------------
y=x+5
-y=x-71
------------
0=x+5
0=x-71
-5-+71=76
------------- this is wrong is it
y=x+5
71=x+y
----------------------
-5=x+-y
71=x+y
66=x CORRECT IT PLease

 

[mg0stisha]

try taking the first equation just as it is, and substituting it in for the 'y' in the second equation.

 

[yuuri14]

try taking the first equation just as it is, and substituting it in for the 'y' in the second equation.

y=x+5
71=x+y

y=x+5
71=x+x+5
71=x2+5
-5 -5
66=x2
8.12=x

IS THIS STILL WRONG?... DO I NEED TO INCORPORATE "The smaller van makes two trips, larger 1 trip".

 

[mg0stisha]

you had everything correct except for your variables. x+x does not equal x^2, it equals 2x. instead of taking the square root, just divide the answer you got by 2.

 

[yuuri14]

you had everything correct except for your variables. x+x does not equal x^2, it equals 2x. instead of taking the square root, just divide the answer you got by 2.

66=2x
33=x

 

[yuuri14]

you had everything correct except for your variables. x+x does not equal x^2, it equals 2x. instead of taking the square root, just divide the answer you got by 2.

then x=33 then back to the situation where the smaller van(x) makes two trips and the question is trying to figure out what's the number of seats on the larger van.

IS THERE ANOTHER STEP BECAUSE WHEN I INPUTTED 33 AS THE ANSWER IT WAS INCORRECT.

A MORE RECENT QUESTION LIKE THIS ONE IS
https://www.physicsforums.com/showthread.php?p=2480814#post2480814

 

[mg0stisha]

well you know that x+y=71
and you now know x, which is the smaller van.
so solve for y! you're almost there.

 

[yuuri14]

well you know that x+y=71
and you now know x, which is the smaller van.
so solve for y! you're almost there.

x=33
x+y=71
33+y=71
-33 -33
y=38 is there another step??

 

[mg0stisha]

if you're just looking for how many seats the larger van has, then no.

 

[yuuri14]

if you're just looking for how many seats the larger van has, then no.

then what do I do?