At a portrait studio, three 8- by 10-inch pictures plus two 5- by -inch pictures cost $52, and two 8- by 10-inch pictures plus 5- by 7-inch pictures cost $40. This situation can represented by the system of equations below, where x is the cost, in dollars, of each 8- by 10-inch picture, and y is the cost of each 5- by 7-inch picture.

Question

At a portrait studio, three 8- by 10-inch pictures plus two 5- by -inch pictures cost $52, and two 8- by 10-inch pictures plus 5- by 7-inch pictures cost $40. This situation can represented by the system of equations below, where x is the cost, in dollars, of each 8- by 10-inch picture, and y is the cost of each 5- by 7-inch picture.
           3x + 2y = 52
           2x + 2y = 40
What is the cost of one 5- by 7-inch picture?
F. $8
G. $10
H. $12
I. $16

Reiny · Accepted Answer

You should be able to do this in your head by just looking at the two equations,

if I subtract them, I get x = 12

look at the second equation, and divide by 2 to get
x + y = 20
well , 12 + what = 20
y has to be 8