Question

8. At a fund raising event, a booth was set up to sell handmade cards and photo

frames. On the first day, 3 cards and 9 photo frames were sold for a total of $75.
The next day, 8 cards and 5 photo frames were sold for a total of $67.
Find the selling price of a card and the selling price of a photo frame.

Answer 1

We can start solving this problem by using a system of equations. Let x be the selling price of a card and y be the selling price of a photo frame.

From the information given, we know that on the first day:

3x + 9y = 75 (1)

And on the second day:

8x + 5y = 67 (2)

Now we have two equations with two variables. To find the value of x and y, we can use either substitution or elimination method.

One possible way to solve for x and y is to use substitution method:

Solve equation (1) for x in terms of y:

x = (75 - 9y) / 3

Substitute this expression into equation (2) to eliminate x:

8((75 - 9y) / 3) + 5y = 67

Solving this equation for y:

y = 3

Now we can substitute this value of y back into equation (1) or (2) to find the value of x:

3x + 9(3) = 75

3x = 48

x = 16

So the selling price of a card is $16 and the selling price of a photo frame is $3.

Answer 2

Photo frame = $7

Card = $4

Explanation:

Define the variables:

• Let c = the selling price of a handmade card (in dollars).
• Let p = the selling price of a handmade photo frame (in dollars).

Given information:

• On the first day, 3 cards and 9 photo frames were sold for a total of $75.
• On the next day, 8 cards and 5 photo frames were sold for a total of $67.

Create a system of linear equations using the given information and defined variables:

`\begin{cases}3c + 9p = 75\\ 8c + 5p = 67\end{cases}`

Rearrange the first equation to isolate c:

`\implies 3c+9p=75`

`\implies 3(c+3p)=75`

`\implies (3(c+3p))/(3)=(75)/(3)`

`\implies c+3p=25`

`\implies c+3p-3p=25-3p`

`\implies c=25-3p`

Substitute the expression for c into the second equation and solve for p:

`\implies 8c+5p=67`

`\implies 8(25-3p)+5p=67`

`\implies 200-24p+5p=67`

`\implies 200-19p=67`

`\implies 200-19p-200=67-200`

`\implies -19p=-133`

`\implies (-19p)/(-19)=(-133)/(-19)`

`\implies p=7`

Therefore, the selling price of a handmade photo frame was $7.

Substitute the found value of p into the expression for c and solve for c:

`\implies c=25-3p`

`\implies c=25-3(7)`

`\implies c=25-21`

`\implies c=4`

Therefore, the selling price of a handmade card was $4.