A class goes on a field trip and the total cost is $240. 4 kids don't go, which increases the cost per kid by $2. How many kids went on the field trip?

Question

Each kid pays equally

Answer 1

The best way to start a problem like this is to write out what we know:

 

240 ÷ the original number of kids = the original cost per kid

240 ÷ (the original number of kids - 4) = (the original cost per kid + 2)

 

Next we pick some abbreviations to make our lives easier. I'll let k stand for the original number of kids and let c stand for the original cost per kid. So now our equations look like this:

 

240 ÷ k = c

240 ÷ (k - 4) = c + 2

 

Now we have two equations for two unknowns, which means we can solve the system. We can use substitution to rewrite the second equation as:

 

240 ÷ (k - 4) = 240 ÷ k + 2

 

And this gets uglier before it gets better:

 

240/(k - 4) = 240/k + 2 → 240/(k - 4) - 240/k = 2 → 240k/(k(k - 4)) - 240(k - 4)/(k(k - 4)) = 2 → 240k - 240(k - 4) = 2(k(k - 4)) → 120k - 120k + 480 = k² - 4k → k² - 4k - 480 = 0

 

This last quadratic equation can be solved either graphically or using the quadratic formula. There will be two solutions, but one of them is negative, which doesn't make sense in the context of counting kids. You should always go back a double check what you solved for, too. Here k was the original number of kids, so the kids that actually end up going is k - 4.

 

 

 

240/k