A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 40 books. A total of 13 boxes were sent which can hold 360 books altogether. Graphically solve a system of equations in order to determine the number of small boxes sent, x, x, and the number of large boxes sent, yy.

Click twice to plot each line. Click a line to delete it.

The Answer is: There are 5 large boxes and 8 small boxes. (The graphical plot will need to be solved using the software).

Step-by-step explanation:

Let xx = small boxes and yy = large boxes:

xx + yy = 13

xx = 13 - yy

The number of small boxes times 20, plus the number of large boxes times 40 is equal to 360:

20xx + 40yy = 360

Substitute the algebraic value of xx, so we only have one variable to consider and solve for yy:

20 (13 - yy) + 40yy = 360

260 - 20yy + 40yy = 360

260 + 20yy = 360

20yy = 100

yy = 100 / 20 = 5 large boxes.

Solve for xx:

xx = 13 - yy

xx = 13 - 5 = 8 small boxes.

There are 5 large boxes and 8 small boxes. (The graphical plot will need to be solved using the software).

Proof:

20xx + 40yy = 360

20 (8) + 40 (5) = 360

160 + 200 = 360

360 = 360