Practice: Models and Applications

Question

A cash register contains only quarters and twenty dollar bills. It contains three times as many quarters as twenty's and the total amount of money in the cash register is $290.50. How many twenty's are in the cash register?

Answer 1

We set up a linear system to solve for this. Because we have two unknown variables, the number of quarters and the number of 20 dollar bills, let's designate them as Q and D.

My first equation relates the combined monetary total of my money with the values of my quarters and bills:

0.25Q + 20D = 290.50, as given in the problem.

My second equation uses the other piece of information given. that there are three times as many quarters are there are bills. Thus, we know 3D = Q.

We can substitute Q for 3D in our first equation to get 0.75D + 20D = 20.75D = 290.50, where we see that D = 14, and plugging this into our second equation, we arrive at Q = 42.