Solve Practical Problems Involving Equations and Systems of Equations

Question

Mrs. Smith bought 4 pencils and 3 pens for $5.60.

       Mr. Brown bought 2 pencils and 3 pens of the same

       kind for $4.60. What is the price of each pencil and

       pen?

Answer 1

Let x be pencils and y be pens

Mrs. Smith bought 4 pencils and 3 pens for $5.60

4x+3y=5.60

 Mr. Brown bought 2 pencils and 3 pens of the same kind for $4.60

2x+3y=4.60

4x+3y=5.60

-(2x+3y=4.60)=-2x-3y=-4.60

add this to the other equation to eliminate y

4x+3y=5.60

-2x-3y=-4.60

2x=1.00

x=0.50 pencils cost 50 cents

to find y plug x=.50 into one of the equations

4(.50)+3y=5.60

2+3y=5.60

Subtract 2 from both sides

3y=3.60

Divide both sides by 3

Y=1.20

Pencils cost $1.20