At a price of $3.20 per bushel, the supply of corn is 9,800 million bushels and the demand is 9,200 million bushels. At a price of $2.95 per bushel, the supply is 9,300 million bushels and the demand is 9,700 million bushels. Find a price–supply equation of the form p = mx + b. p is in dollars, and x is in million bushels.

At a price of $3.20 per bushel, the supply of corn is 9,800 million bushels and the demand is 9,200 million bushels. At a price of $2.95 per bushel, the supply is 9,300 million bushels and the demand is 9,700 million bushels. Find a price–supply equation of the form p = mx + b. p is in dollars, and x is in million bushels.

Question
Equations and inequalities
asked 2020-10-19
At a price of $3.20 per bushel, the supply of corn is 9,800 million bushels and the demand is 9,200 million bushels. At a price of $2.95 per bushel, the supply is 9,300 million bushels and the demand is 9,700 million bushels. Find a price–supply equation of the form p = mx + b. p is in dollars, and x is in million bushels.

Answers (1)

2020-10-20
If p is price per bushel and xx is supply (in million bushels), then it must be true that
\(\displaystyle{3.20}={9800}{m}+{b}\)
\(\displaystyle{2.95}={9300}{m}+{b}\)
Subtracting these two equations, we get
\(\displaystyle{0.25}={500}{m}\)
Divide both sides by 500 to get \(\displaystyle{m}={0.00055}.\)
Now substitute this into the first equation to get
\(\displaystyle{3.20}={9800}⋅{0.0005}+{b}\)
\(\displaystyle{3.20}={4.9}+{b}\)
Subtract 4.9 on both sides to get \(\displaystyle{b}=−{1.7}\)
Now that we know both parameters, we can write down the general form
\(\displaystyle{p}={0.0005}{x}−{1.7}\)
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