Question

Hi I need help with question 3 :) . Directions: For each real world situation, write and solve a system of equations . Give the solution as either an ordered pair or list what each variable is worth . Then explain what the solution means in terms of the situation

Answer 1

3.

We know that Hobby Land sells art supplies two different ways.

We can represent the situation with a system of equations

`\begin{cases}x+y=139\ldots(1) \\ 4x+7y=781\ldots(2)\end{cases}`

Where x is the cost of one easel and y represents the cost of one paint set.

Now, we must solve the system of equations.

We can multiply equation (1) by -4

`\begin{gathered} -4(x+y)=-4(139) \\ -4x-4y=-556\ldots(3) \end{gathered}`

Then, we can add (3) + (2)

`\begin{gathered} -4x-4y=-556 \\ 4x+7y=781 \\ -------------- \\ 3y=225 \end{gathered}`

Now, we can solve the equation for y

`\begin{gathered} 3y=225 \\ y=(225)/(3)=75 \end{gathered}`

Finally, to find x we can replace the value of y in the equation (1)

`\begin{gathered} x+75=139 \\ x=139-75=64 \end{gathered}`

So, the cost of one easel is $64.

Solution as either an ordered pair:

- (64, 75).