Answer: 161 packages of gift wrap and the 44 packages of greeting cards
Step-by-step explanation:
We are told the class sells 205 packages in total of gift wraps and greting cards:
[tex]205=x+y[/tex] (1)
Where [tex]x[/tex] is the number of packages of gift wrap and [tex]y[/tex] is the number of packages of greeting cards.
In addition, we are told the class receives a total of [tex]\$1084[/tex] selling each package of gift wrap for [tex]\$4[/tex] and each package of greeting cards for [tex]\$10[/tex]:
[tex]1084=4x+10y[/tex] (2)
Isolating [tex]x[/tex] from (1):
[tex]x=205-y[/tex] (3)
Substituting (3) in (2):
[tex]1084=4(205-y)+10y[/tex] (4)
Finding [tex]y[/tex]:
[tex]y=44[/tex] (5) This is the number of packages of greeting cards
Substituting (5) in (1):
[tex]205=x+44[/tex] (6)
Isolating [tex]x[/tex]:
[tex]x=161[/tex]This is the number of packages of gift wrap
