Question

I'm trying to find out the number of how much it cost to wrap each present, day one 41 small gifts were wrapped and 45 large were wrapped equaling $397, day two 30 small gifts were wrapped and 47 large were wrapped equaling $389

Answer 1

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:

$41x+45y=397...(1)$

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:

$30x+47y=389...(2)$  

From equation (1), we will get:

$x=\frac{397-45y}{41}$

Upon substituting this value in equation (2), we will get:

$30(\frac{397-45y}{41})+47y=389$

$\frac{11910-1350y}{41}+\frac{47*41y}{41}=389$

$\frac{11910-1350y+1927y}{41}=389$

$\frac{11910+577y}{41}=389$

$\frac{11910+577y}{41}\cdot 41=389\cdot 41$

$11910+577y=15949$

$11910-11910+577y=15949-11910$

$577y=4039$

$\frac{577y}{577}=\frac{4039}{577}$

$y=7$

Therefore, cost to wrap a large gift is $7.

Upon substituting $y=7$ in equation $x=\frac{397-45y}{41}$, we will get:

$x=\frac{397-45(7)}{41}$

$x=\frac{397-315}{41}$

$x=\frac{82}{41}$

$x=2$

Therefore, cost to wrap a small gift is $2.