writing utensils\nmiss farnsworth has noticed that several of her students have been coming to class without…

writing utensils\nmiss farnsworth has noticed that several of her students have been coming to class without pens or pencils. so she has decided to start selling them in class. terrence decided to buy 2 pencils and 3 pens for a total of $1.55. erica purchased 3 pencils and 4 pens for the price of $2.15.\nwrite a system of equations to model terrences and ericas purchases and then determine the cost of a pencil and the cost of a pen.
Answer
Explanation:
Step1: Define variables
Let (x) be the cost of a pencil and (y) be the cost of a pen.
Step2: Set up equations
For Terrence: (2x + 3y=1.55) For Erica: (3x + 4y = 2.15)
Step3: Solve the system
Multiply the first equation by (3): (6x+9y = 4.65) Multiply the second equation by (2): (6x + 8y=4.3) Subtract the second new equation from the first: ((6x + 9y)-(6x + 8y)=4.65 - 4.3) (y=0.35) Substitute (y = 0.35) into (2x+3y = 1.55): (2x+3\times0.35=1.55) (2x+1.05 = 1.55) (2x=1.55 - 1.05) (2x=0.5) (x = 0.25)
Answer:
The cost of a pencil is ($0.25) and the cost of a pen is ($0.35)