The numbers line? The money line?

Question

A group of friends attend a zip line adventure birthday party. Each person pays $40 for the zip line pass, and they order a bunch of pizzas for $10 each. If the total bill for the party was $1100, and the number of kids that attended the party and the number of pizzas that were ordered totalled 38, then find the number of people that attended the party and the number of pizzas that they ordered.

Answer 1

Let's set up our two equations. Each friend, which we'll use the variable F, paid $40, and they ordered some number of pizzas for $10 each for a total of $1100, so 40F + 10P = 1100. Let's isolate the variable F by first subtracting both sides by 10P. 40F = 1100 - 10P. Now, we divide both sides by 40 and F = (1100/40) - 10/40P, or F = 27.5 - 1/4P.

The number of kids that attended the party (F) and the number of pizzas ordered (P) totals 38, so our second equation is F + P = 38. Let's isolate F in this equation, too, by subtracting both sides by P, so F = 38 - P.

Now, we substitute what F equals in our second equation for F in our first equation, and 38 - P = 27.5 - 1/4P. Simplifying by adding P to both sides, 38 = 27.5 + 3/4P. Subtracting 27.5 from both sides, we get 10.5 = 3/4P. Dividing both sides by 3/4 (i.e. multiplying both sides by 4/3) we get P = 14.

Now, we can solve for F. F = 38 - P, or 38 - 14, so F = 24. The number of people that attended the party was 24 and the number of pizzas they ordered was 14!