document.write( "Question 858276: The demand function for a particular product is given by p + 10q = 460 while supply for the product is given by p - 10q = -240\r
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Algebra.Com's Answer #517163 by math-vortex(648)\"\" \"About 
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document.write( "Hi there,\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "The demand function for a particular product is given by p + 10q = 460 while supply for the product is\r\n" );
document.write( "given by p - 10q = -240\r\n" );
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document.write( "a) Find the market equilibrium quantity and price\r\n" );
document.write( "b) If the price per product is set at $50, will there be a shortage or a surplus in the market?\r\n" );
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document.write( "SOLUTION:\r\n" );
document.write( "Part (a)\r\n" );
document.write( "Equilibrium quantity and price are found at the point the equations for supply and demand intersect. \r\n" );
document.write( "To find these values, solve the two equations as a system. In this case, you can solve by the substitution \r\n" );
document.write( "method.\r\n" );
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document.write( "Step 1. Solve both equations for p.\r\n" );
document.write( "p + 10q = 460\r\n" );
document.write( "p = -10q + 460\r\n" );
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document.write( "p - 10q = -240\r\n" );
document.write( "p = 10q - 240\r\n" );
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document.write( "Step 2. Since p equals -10q+460 AND p equals 10q-240, those quantities must also be equal to each \r\n" );
document.write( "other. (This is called the Transitive Property.) Set them equal to each other and solve for q.\r\n" );
document.write( "-10q + 460 = 10q -240\r\n" );
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document.write( "Subtract 10q from both sides.\r\n" );
document.write( "-10q -10q + 460 = -10q + 10q -240\r\n" );
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document.write( "Combine like terms and simplify.\r\n" );
document.write( "-20q + 460 = -240\r\n" );
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document.write( "Subtract 460 from both sides.\r\n" );
document.write( "-20q +460 - 460 = -240 - 460\r\n" );
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document.write( "Combine like terms and simplify.\r\n" );
document.write( "-20q = -700\r\n" );
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document.write( "Divide both sides by -20.\r\n" );
document.write( "-20q/-20 = -700/-20 \r\n" );
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document.write( "Simplify.\r\n" );
document.write( "q = 35\r\n" );
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document.write( "In the context of this problem, q = 35 means that the equilibrium quantity is 35 units of the product.\r\n" );
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document.write( "Step 3. Now substitute 35 for q in either one of the original equations. (I'll use the first.)\r\n" );
document.write( "p + 10q = 460\r\n" );
document.write( "p + 10(35) = 460\r\n" );
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document.write( "Simplify.\r\n" );
document.write( "p + 350 = 460\r\n" );
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document.write( "Subtract 350 from both sides.\r\n" );
document.write( "p + 350 - 350 = 460 - 350\r\n" );
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document.write( "Combine like terms and simplify.\r\n" );
document.write( "p = 110\r\n" );
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document.write( "In the context of this problem, p = 110 means that the equilibrium price is $110 for each unit of the \r\n" );
document.write( "product.\r\n" );
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document.write( "Part (b)\r\n" );
document.write( "In this case we want to know how a price of $50 will effect supply and demand. If supply is greater than \r\n" );
document.write( "demand, there is a surplus. If supply is less than demand, there is a shortage.\r\n" );
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document.write( "Step 1. Substitute $50 for p in the Supply and demand equations.\r\n" );
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document.write( "DEMAND: \r\n" );
document.write( "p + 10q = 460 \r\n" );
document.write( "(50) + 10q = 460\r\n" );
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document.write( "Subtract 50 from both sides.\r\n" );
document.write( "10q = 460 - 50\r\n" );
document.write( "10q = 410\r\n" );
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document.write( "Divide both sides by 10.\r\n" );
document.write( "q = 41\r\n" );
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document.write( "When the the price is set at $50, the market demand is 41 units of product.\r\n" );
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document.write( "SUPPLY:\r\n" );
document.write( "p - 10q = -240\r\n" );
document.write( "(50) - 10q = -240\r\n" );
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document.write( "Subtract 50 from both sides.\r\n" );
document.write( "-10q = -240 - 50\r\n" );
document.write( "-10q = -290\r\n" );
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document.write( "Divide both sides by -10.\r\n" );
document.write( "q = 29\r\n" );
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document.write( "When the price is set at $50, the market supply is 29 units of product.\r\n" );
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document.write( "Since the supply of product (29) is less than the demand for product (41), there is a shortage.\r\n" );
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document.write( "Hope this helps. Feel free to email if you have questions about the solution.\r\n" );
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document.write( "Mrs. Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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