Linear System Application

Question

I have a word problem where there is a zoo which charges adults $34 and children $24. A total of 108,840 was collected from 3960 admissions. How may adults and how many children. I just want to to understand th equation and steps to solve;

The equation would be adults=x, children=y

x+y=3960

34x + 24y=108,840

Where would I go in terms of next steps, would I solve for above?

Answer 1

You can solve these two equations with two unknowns using substitution.

First let's solve the first equation for y as follows:

x + y = 3960

Subtract x from both sides of the equation:

x + y - x = 3960 - x

Then y = 3960 - x

Now we can substitute this expression for y in the second equation and solve for the value of x:

34x + 24y = 108840

34x + 24(3960 - x ) = 108840

Now use the distributive property as follows:

34x + 95040 - 24x = 108840

Now we can combine like terms and use inverse operations to solve for x:

10x + 95040 = 108840

10x + 95040 - 95040 = 108840 - 95040

10x = 13800

10x/10 = 13800/10

x = 1380 tickets for adults

Since x + y = 3960, y will be 3960 - 1380 OR y = 2580 tickets for children

Hope this helps!