Question

You went shopping for back to school and bought packs of pens and pencils. a pack of

pencils cost $2.50 and a pack of pens cost $3. you spent a total of $35 and bought a
total of 13 packs. how many packs of pencils and how many packs of pens did you
buy?

Answer 1

5 packs of pens and 8 packs of pencils.

Explanation:

Let the Pn and Pl stand for the number of packs of pens (Pn) and pencils (Pl) purchased.

We know that each pack of pens is $3 and each pack of pencils is $2.50.

We are also told that Pn + Pl = 13 [In total, 13 packs were purchased].

And we're told that $35 was spent.

The $35 must equal: $3*Pn + $2.5*Pl [the sum of the number of packs of each times the price per pack for each]

3*Pn + 2.5*Pl = 35

Rearrange the first equation:

Pn + Pl = 13

Pn = 13 - Pl

Use this definition of Pn in the second equation:

3*Pn + 2.5*Pl = 35

3*(13 - Pl) + 2.5*Pl = 35

39 - 3Pl + 2.5Pl = 35

-0.5Pl = -4

Pl = 8

8 packs of pencils (Pl) were purchased.

This means the packs of pens purchased must be 5, since a total of 13 packs were purchased.

Check:

Does 5 packs of pens and 8 packs of pencils total $35?

5*($3) + 8*($2.5) = $35 ??

$15 + $20 = $35 ?

YES

You bought 5 packs of pens and 8 packs of pencils.