Problem

Last year, Pinwheel Industries introduced a new toy. It cost $\$ 4400$ to develop the toy and $\$ 35$ to manufacture each toy. Fill in the blanks below as appropriate.

A.) Give a linear equation in the form $C=m n+b$ that gives the total cost, $C$, to produce $n$ of these toys:
\[
C=
\]
B.) The total cost to produce $n=2550$ toys is $\$$
C.) With $\$ 128650$, a total of toys can be produced.

Answer

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Answer

\(\boxed{\text{A.) The linear equation that gives the total cost, } C, \text{ to produce } n \text{ of these toys is } C = 35n + 4400.\text{ B.) The total cost to produce } n=2550 \text{ toys is } \$93650. \text{ C.) With } \$128650, \text{ a total of } 3550 \text{ toys can be produced.}}\)

Steps

Step 1 :Translate the given problem into a linear equation. The cost to develop the toy is a fixed cost, which is the y-intercept (b) in our equation. The cost to manufacture each toy is the slope (m), as this cost is multiplied by the number of toys produced (n). So, the equation would be \(C = 35n + 4400\).

Step 2 :Substitute \(n = 2550\) into our equation to find the total cost. The total cost to produce 2550 toys is \(C = 35 \times 2550 + 4400 = 93650\).

Step 3 :Solve the equation for n when \(C = 128650\). With \(128650\) dollars, a total of \(\frac{128650 - 4400}{35} = 3550\) toys can be produced.

Step 4 :\(\boxed{\text{A.) The linear equation that gives the total cost, } C, \text{ to produce } n \text{ of these toys is } C = 35n + 4400.\text{ B.) The total cost to produce } n=2550 \text{ toys is } \$93650. \text{ C.) With } \$128650, \text{ a total of } 3550 \text{ toys can be produced.}}\)

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