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)

Question

Mathematics

Makenna Santana

22 March, 02:30

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)

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Answers (1)

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Octavio Hammond · Answer 1

0.50x+1.50y=12

x+y=16

At the store you buy 12 pencils for $0.50 and 4 pens for $1.50. The total is $12 and 16 items.

Equation

0.50x+1.50y=12

0.50x=-1.5y+12

x=-3+24

(-3y+24) + y=16

-3y+24+y=16

-2y=-8

y=4

x+4=16

x=12

x=12 y=4