Answer :
Answer:
Small gift: $2
Large gift: $7
Step-by-step explanation:
Let x represent cost of wrapping each small gift and y represent cost of wrapping each large gift.
We have been given that day one 41 small gifts were wrapped and 45 large were wrapped equaling $397.
We can represent this information in an equation as:
[tex]41x+45y=397...(1)[/tex]
We are also told that day two 30 small gifts were wrapped and 47 large were wrapped equaling $389. We can represent this information in an equation as:
[tex]30x+47y=389...(2)[/tex]
From equation (1), we will get:
[tex]x=\frac{397-45y}{41}[/tex]
Upon substituting this value in equation (2), we will get:
[tex]30(\frac{397-45y}{41})+47y=389[/tex]
[tex]\frac{11910-1350y}{41}+\frac{47*41y}{41}=389[/tex]
[tex]\frac{11910-1350y+1927y}{41}=389[/tex]
[tex]\frac{11910+577y}{41}=389[/tex]
[tex]\frac{11910+577y}{41}\cdot 41=389\cdot 41[/tex]
[tex]11910+577y=15949[/tex]
[tex]11910-11910+577y=15949-11910[/tex]
[tex]577y=4039[/tex]
[tex]\frac{577y}{577}=\frac{4039}{577}[/tex]
[tex]y=7[/tex]
Therefore, cost to wrap a large gift is $7.
Upon substituting [tex]y=7[/tex] in equation [tex]x=\frac{397-45y}{41}[/tex], we will get:
[tex]x=\frac{397-45(7)}{41}[/tex]
[tex]x=\frac{397-315}{41}[/tex]
[tex]x=\frac{82}{41}[/tex]
[tex]x=2[/tex]
Therefore, cost to wrap a small gift is $2.