the senior class at highschool a and highschool b planned separate trips to the local amusement park the senior class at highschool a rented and filled 5 vans and 8 buses with 357 students highschoolb rented and filled 10 vans and 5 buses with 285 students every van had the same number of students in it as did the buses find the number of students in each vans and in each bus
solve:
5v + 8b = 357
10v + 5b = 285 --- > 2v + b = 57
then b = 57-2v
sub into the first
5v + 8(57-2v) = 357
5v - 16v = -99
v = -99/-11 = 9
then b= 57-2(9) = 39
A van holds 9 students and a bus holds 39 students
Your post is too difficult to read because it lacks punctuation and capitalization.
Let's assume that each van has the same number of students, denoted by "v", and each bus also has the same number of students, denoted by "b".
From the given information, we can create two equations:
Equation 1: 5v + 8b = 357 (for Highschool A)
Equation 2: 10v + 5b = 285 (for Highschool B)
We can solve this system of equations using substitution or elimination method. Let's use the elimination method to solve it:
Multiply Equation 1 by 2:
10v + 16b = 714
Now, subtract Equation 2 from the adjusted Equation 1:
10v + 16b - (10v + 5b) = 714 - 285
10v + 16b - 10v - 5b = 429
11b = 429
Divide both sides of the equation by 11:
b = 39
Now substitute the value of "b" into Equation 1 or Equation 2:
5v + 8(39) = 357
5v + 312 = 357
5v = 357 - 312
5v = 45
Divide both sides of the equation by 5:
v = 9
Therefore, each van had 9 students, and each bus had 39 students.
To solve this problem, let's represent the number of students in each van with the variable 'v' and the number of students in each bus with the variable 'b'.
We know that the senior class at high school A rented and filled 5 vans and 8 buses with a total of 357 students. This can be expressed as the equation:
5v + 8b = 357 ----(1)
Similarly, the senior class at high school B rented and filled 10 vans and 5 buses with a total of 285 students. This can be expressed as the equation:
10v + 5b = 285 ----(2)
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the method of elimination to eliminate the variable 'b'.
Multiply equation (1) by 5 and multiply equation (2) by 8 to make the coefficients of 'b' equal.
25v + 40b = 1785 ----(3)
80v + 40b = 2280 ----(4)
Now, subtract equation (3) from equation (4) to eliminate 'b':
(80v + 40b) - (25v + 40b) = 2280 - 1785
55v = 495
Divide both sides of the equation by 55:
v = 495 / 55
v = 9
Now substitute the value of 'v' back into one of the original equations (let's use equation (1)) to find the value of 'b':
5(9) + 8b = 357
45 + 8b = 357
Subtract 45 from both sides of the equation:
8b = 357 - 45
8b = 312
Divide both sides of the equation by 8:
b = 312 / 8
b = 39
Therefore, there are 9 students in each van and 39 students in each bus.