Question

All of the 11™ grade teachers and students from gorton went on a trip to a math museum. tickets were $22.00 each for teachers and $8.50 each for students, and the group paid $173.00 in total. a few weeks later the same group visited an art museum where the tickets cost $5.50 each for teachers and $2.00 each for students, and the group paid $42.00 in total. find the number of teachers and students on the trips.

Answer 1

The number of teachers is 4 and number of students is 10 on the trips if the tickets were $22.00 each for teachers and $8.50 each for students.

What is 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 the linear equation in one variable.

We have:

In Maths museum tickets were $22.00 each for teachers and $8.50 each for students, and the group paid $173.00 in total.

Let's suppose the number of teachers is x and number of students is y

22x + 8.5y = 173 ...(1)

5.5x + 2y = 42  ...(2)

After solving the above equation by substitution method we get;

From equation (1):

Multiply by 2 with equation (1)

$\rm x=\dfrac{346-17y}{44}$

$\rm 5.5\cdot \dfrac{346-17y}{44}+2y=42$

y = 10

$\rm x=\dfrac{346-17\cdot \:10}{44}$

x = 4

Thus, the number of teachers is 4 and number of students is 10 on the trips if the tickets were $22.00 each for teachers and $8.50 each for students.

Learn more about the linear equation here:

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