The senior classes at Downingtown HS and West Chester HS planned separate trips to Top Golf. The senior class at Downingtown rented and filled 14 vans and 7 buses with 476 students. West Chester HS rented and filled 7 vans and 11 buses with 628 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry?

The van can carry 8 students

The bus can carry 52 students

Step-by-step explanation:

Assume that the number of students in each van is v and the number of students in each bus is b

∵ The senior class at Downingtown rented and filled 14 vans and

   7 buses with 476 students

∵ The number of students in each van is v

∵ The number of students on each bus is b

∴ 14v + 7b = 476 ⇒ (1)

∵ West Chester HS rented and filled 7 vans and 11 buses with

   628 students

∴ 7v + 11b = 628 ⇒ (2)

Let us solve this system of equations to find v and b

→ Multiply equation (2) by -2 to make the coefficients of v equal in

  the values and different in the signs

∵ -2(7v) + -2(11b) = -2(628)

∴ -14v - 22b = -1256 ⇒ (3)

→ Now add equations (1) and (3) to eliminate v

∴ -15b = -780

→ Divide both sides by -15

∴ b = 52

→ Substitute the value of b in equation (1) to find v

∵ 14v + 52(7) = 476

∴ 14v + 364 = 476

→ Subtract 364 from both sides

∴ 14v = 112

→ Divide both sides by 14

∴ v = 8

The van can carry 8 students

The bus can carry 52 students

Complete question is;

A square pyramid has side lengths each measuring 8 centimeters. The height of the pyramid is 3 centimeters. What is the lateral area of the pyramid?

Lateral area = 80 cm²

Step-by-step explanation:

We are given;

Side length; a = 8 cm

Height of pyramid; h = 3 cm

Now, formula for Lateral area of pyramid = ½ × p × L

Where p is perimeter of base and L is slant length.

Since we know the side length and height of pyramid, we can find the slant height using Pythagoreas theorem.

L² = (½×side length)² + h²

L² = (½×8)² + 3²

L² = 16 + 9

L = √25

L = 5 cm

Now perimeter of square base = 4a = 4 x 8 = 32cm

So,

Lateral area = ½ × p × L = ½ × 32 × 5

Lateral area = 80 cm²