Answer:
5 packs of pens and 8 packs of pencils.
Step-by-step 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.
