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The seniors and juniors at Sweet Valley High School are going on a trip to Busch
Gardens. The seniors filled 12 vans and 12 buses with 564 total students. The juniors
filled 6 vans and 13 buses with 492 students. How many students were in each van? In
each bus?

Solve the system of equations

Respuesta :

Answer:

buses can hold 30 and vans can hold 17.

Step-by-step explanation:

Let the amount a van can hold be v and the amount a bus can hold be b.

12 vans and 12 buses totals 564: 12v + 12b = 564 (equation 1)

6 vans and 13 buses totals 492: 6v + 13b = 492 (equation 2)

Subtract 2 times equation 2 from equation1, we get 14b = 420.

Thus, b = 30.

Since 12v + 12b = 564, plugging in b=30, 12v + (12)(30) = 564, so v = 17.

The number of students filled in the van is 17, and number of students filled in the bus is 30.

What is a linear equation?

It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.

If in the linear equation one variable is present then the equation is known as linear equation in one variable.

Let's suppose the total number of students in van is x, and the number of students in the bus is y

Now for the first scenario we can frame a linear equation in two variables such as:

12x + 12y = 564 or

x + y = 47  ....(1)  (divide by 12 on both sides)

For the second scenario the linear equation in two variables becomes:

6x + 13y = 492 ....(2)

From the equation (1) take the value of x and plug in the equation (2), we get:

6(47-y) + 13y = 492

282 - 6y +13y = 492

7y = 492-282   (subtract 282 from both sides)

7y = 210

y = 30

Put this value in the equation (1), we get:

x + 30 = 47

x = 17   (subtract by 30 from both sides)

Thus, the number of students filled in the van is 17, and number of students filled in the bus is 30.

Learn more about the linear equation here:

brainly.com/question/11897796

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