Two students are going to the store to buy school supplies for the new school year. One of the students buys 2 packs of pencils and 3 packs of pens for $8.25. Her friend purchases 5 packs of pencils and 2 packs of pens for $11.00. Is there enough information to determine the cost of 1 pack of pencils and 1 pack of pens? If so, find the cost of each. Explain your thinking.

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[tex]10x+15y=41.25\\10x=4y=22 \\[/tex]

Subtract the resulting equations;

[tex]15y-4y=41.25-22\\11y=19.25\\y=19.25/11\\y= $ 1.75 \\[/tex]

Hence 1 pack of pen costs %1.75

To get x, you will substitute y= 1.75 into equation 2;

[tex]2;5x+2y=11\\5x+2(1.75)=11\\5x+3.5=11\\5x=11-3.5\\5x=7.5\\x=\frac{7.5}{5} \\x=1.5[/tex]

Hence 1 pack of pencil will cost costs $1.5

From the above solution, we can conclude that there are enough information to find the cost of each pack of pen and pencil.

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goodmorningbeautiful goodmorningbeautiful · Answer 2 · 2020-12-16T20:19:35+01:00

Let the unit price for pencil be x

Let the unit price for pack be y

If the students bought 3 packs of pencil and 2 packs of pen for $8.25, then;

Similarly;

If her friend bought 5 packs of pencil and 2 packs of pen for $11, then ;

We will have to solve both equations simultaneously as shown;

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Subtract the resulting equations;

Hence 1 pack of pen costs %1.75

To get x, you will substitute y= 1.75 into equation 2;

Hence 1 pack of pencil will cost costs $1.5

From the above solution, we can conclude that there are enough information to find the cost of each pack of pen and pencil.