New York City is a popular field trip destination. THis year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 1 van and 6 buses with 324 students. High School B rented and filled 9 van and 3 busses with 264 students. How many students can a van carry? How many students can a bus carry?

number of students in a van=12

number of students in a bus=52

Step-by-step explanation:

let number of students in a van=x

number of students in a bus=y

1x+6y=324     ...(1)

9x+3y=264   ...(2)

multiply (2) by 2

18x+6y=528   ...(3)

(3)-(1) gives

17x=204

x=204/17=12

put in (1)

12+6y=324

6y=324-12=312

y=312/6=52

answer: ♡♡♡♡♡♡♡♡♡♡

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4