6) Fadel owns a small business that manufactures and sells clocks. The clocks cost $12.50 each to manufacture with a monthly overhead of $4500. Fadel sells the clocks for $37.50 each (5pts each) a) Analyze and set-up a cost equation and a revenue equation for these clocks. b) Find the cost and how many clocks Fadel needs to make and sell to break-even. 7) Sia owns a candy store, and she wants to mix gummy worms worth $3 per pound with gummy bears worth $1.50 per pound to make 30 pounds of a mixture worth $63.00. (Spts each) a) Analyze and set-up a system of equations for this mixture (quantity-value system). b) Solve this system of equations to determine how many pounds of each of candy Sia should use for this mixture.

We are told that one point of gummy worms costs $3, meaning w pounds cost 3 *w. Moreover, one pound of gummy worms costs $1.5, meaning b pounds ost 1.5 * b.

The total worth of the gummies is $63; therefore,

[tex]3w+1.5b=63[/tex]

Also, we know that the total number of pounds of gummies is 30 pounds; therefore,

[tex]w+b=30[/tex]

Hence, we have the system

[tex]\begin{cases}w+b=30 \\ 3w+1.5b=63\end{cases}[/tex]

Part B:

To solve the system given above, we first solve for w in the first equation.

[tex]w+b=30[/tex][tex]\rightarrow w=30-b[/tex]

We put the value of the w given above into the second equation to get

[tex]\begin{gathered} 3w+1.5b=63 \\ \rightarrow3(30-b)+1.5b=63 \end{gathered}[/tex][tex]=90-3b+1.5b=63[/tex][tex]90-1.5b=63[/tex]

subtracting 90 from both sides gives

[tex]-1.5b=-27[/tex]

Finally, dividing both sides by -1.5 gives

[tex]\boxed{b=18}[/tex]

With the value of b in hand, we now put it into w + b = 30 and solve for w to get

[tex]w+18=30[/tex][tex]w=30-18[/tex][tex]\boxed{w=12}[/tex]

Hence, the solution to the system is w = 12, b = 18.