Ben James is studying monthly demand for Chevrolet Impalas in two different regions of the country. He has 14,200 new Impalas to ship to the two regions, and he decides to ship 3350 more to the Southeast region than to the mid–Atlantic Coast region. Find the number to be shipped to the mid–Atlantic

Question

Ben James is studying monthly demand for Chevrolet Impalas in two different regions of the country. He has 14,200 new Impalas to ship to the two regions, and he decides to ship 3350 more to the Southeast region than to the mid–Atlantic Coast region. Find the number to be shipped to the mid–Atlantic Coast region.

CASE IN POINT Let m = number of Impalas to be shipped to the mid–Atlantic Coast region. Then (m + 3350) = number to be shipped to the Southeast region. The sum of the two shipments is 14,200.

Accepted Answer

[latex]\begin{matrix} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ^{\mathbf{Number\ to}}_{\underset{\mathbf{Coast\ region\ \ \ \ \ \ \ \ \ }} {\mathbf{mid–Atlantic}}}& \ \ \ \ \ \ \ \ \ \mathbf{+} & \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ^{\mathbf{ \ \ \ \ \ \ Number\ to}}_ {\mathbf{{Southeast\ region}}}\ \ \ \ \ = \ \mathbf{Total} & \ \ \ \ \ \ \ \ \ \ \ \ \ m & \ \ \ \ \ \ \ \ \ + & \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (m + 3350) = 14,200 & \ & & \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ m + m + 3350 = 14,200 & \mathbf{Remove\ parentheses}\ & & \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2m + 3350 = 14,200 & \mathbf{Combine\ like\ terms.}\ & & \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2m + 3350\ \mathbf{−\ 3350} = 14,200\ \mathbf{−\ 3350} & \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \mathbf{Subtract\ 3350\ from\ both\ sides.} \ & & \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2m = 10,850 & \mathbf{Simplify.}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ & & \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{2m}{2} = \frac{10,8502}{2}& \mathbf{ \ \ \ \ \ \ Divide\ both\ sides\ by\ 2.} \ \ & & \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ m = 5425 & \end{matrix}[/latex]

So the numbers to be shipped are

m = 5425 to the mid-Atlantic Coast region

(m + 3350) = [latex]\underline{\ \ 8775}[/latex] to the Southeast region

= 14,200 to be shipped

Since this agrees with the total to be shipped, the answer checks.

Question 4.2.6: Ben James is studying monthly demand for Chevrolet Impalas i......

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