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21 January, 16:16

The cost, C, in millions of dollars of producing T million tons of steel is modeled by the equation C = 220T + 1890.

Solve the equation for T.

The steel produced is expected to be sold at a price of $310 per ton. Write and solve an equation to find the amount of steel produced if the selling price is equal to the cost of production.

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  1. 21 January, 16:26
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    C = 220T + 1890.

    Solve the equation for T.

    220T = C - 1890

    T = C/220 - 8.6

    The steel produced is expected to be sold at a price of $310 per ton.

    310 $/ton is a rate or slope. Write a linear equation where x is tons of steel produced and y is selling price of the steel.

    y = 310x

    Write and solve an equation to find the amount of steel produced if the selling price is equal to the cost of production.

    * Here, note that the cost of production and tons of steel in the first equation is in the millions. The equation we just wrote for the selling price was in x tons of steel. This only matters in regards to the units you specify because; million/million = 1

    The unit multiplier of all variables must be specified as same. Either everything is in millions or not.

    Here, I'll leave everything in millions, change x (tons of steel) to T (mill tons steel) and "y" to "S" in million dollars selling price.

    S = 310T

    Set equal to Cost equation.

    220T + 1980 = 310T

    Solve for T, million tons of steel produced.

    1980 = 310T - 220T

    1980 = 90T

    T = 1980/90

    T = 22 million tons steel produced
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