At the store, you buy some pencils for $0.50 each and some pens for $1.50 each. you spend a total of $12 and purchase 16 items (pencils and pens only). (a) write and solve a system of equations that model the problem. show all your work (b) how many of each type of writing utensil did you purchase? (write your answer in a complete sentence)

(A) Let p represent the number of pencils and n represent the number of pens you bought.
.. p + n = 16 . . . . . . . . . . . . . . . you bought 16 items
.. .50p +1.50n = 12.00 . . . . . . the amount you spent was $12

Subtract the first equaton from twice the second
.. 2(.50p +1.50n) -(p +n) = 2(12.00) -(16)
.. 2n - 8
.. n = 4
.. p = 16 -n = 12

(B) You bought 12 pencils and 4 pens.