Marcella and Danilo went to a bookstore. Marcella bought 2 notebooks and 3 pens for $14.50. Danilo bought 1 notebook and 2 pens for $7.50. How much does 1 notebook cost?

equation 1: 2N+3P=14.50

equation 2: 1N + 2P = 7.50

multiply equation 2 by 2 so that N is same as equation 1

1N+2P=7.50 x 2 = 2N+4P = 15.00

subtract equation 1 from new equation

2N+4P = 15.00 - 2N+3P=14.50 = 1P = 0.50

so 1 pen cost 0.50

replace 0.50 for P in equation 1:

2N+3P=14.50 =

2N + 3 (0.50) = 14.50

2N + 1.50 = 14.50

2N = 13.00

N=13.00/2 = 6.50

notebook cost 6.50

check:

2 (6.50) + 3 (0.50) = 13 + 1.50 = 14.50

1 (6.50) + 2 (0.50) = 6.50 + 1.00 = 7.50

both equations work

Pens cost 0.50 each

notebooks cost 6.50 each