Question

gabby and sydney bought some pens and pencils. Gabby bought 4 pencils for $6.71. Sydney bought 5 pens and 3 pencils for $7.12. Find the cost of each

Answer 1

X=1.19 and Y=.39

Pens=1.19 and pencils=.39

In coordinates: (1.19, .39)

Explanation:

I believe the commentator miswrote a common problem that is state assessment released question if your problem states instead:

Gabby and Sydney bought some pens and pencils. Gabby Bought 4 pens [AND 5 PENCILS] for 6.71. Sydney bought 5 pens and 3 pencils for 7.12. Find the cost of Each.

The word problem gives 2 equations solve by...

Process of Elimination:

X= pens and Y= Pencils

5x + 3y = 7.12

4x + 5y = 6.7

BUT.. you need a common coefficient so you must multiply

Solving for x before y, is most helpful

You must multiply the Y variable to the whole equation on both but with opposites

5(5x + 3y = 7.12)

3(4x + 5y = 6.7)

Your equation should now be..

25x + 15y = 33.60

12x + 15y = 20.10

Now you have a common coefficient, 15 y - itself is 0

now you have 25x-12x=13x and 35.60-20.10

13x=15.5

divide 13 by 15.5 and get 1.19

x=1.19

now plug this x into the Y spot in ANY of both equations

I'm choosing 12x+15y=20.10

now it should be 12(1.19) + 15y = 20.10

making y = .388 rounded is .39 cents

Answer 2

Given that Gabby bought 4 pencils for $6.71 in total, this would mean that each pencil costs $1.68. On the other hand, Sydney bought 5 pens and 3 pencils with a total of $7.12. In this case, we multiply $1.68 by 3 and the total is $5.03. Now, deduct 5.03 from 7.12 and the answer is $2.09. So $2.09 is the total amount of pens, and each pen costs $0.42. Hope this answers your question.