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We have two unknowns: the price of a color cartridge and the price of a black ink cartridge. First we will use two variables for these unknowns so we will need two equations.
\n" ); document.write( "Let c = price of a color cartridge
\n" ); document.write( "Let b = the price of a black ink cartridge.
\n" ); document.write( "From \"A color cartridge for xt-100 inkjet printer is $5 more than twice the price of a black ink cartridge.\" we get:
\n" ); document.write( "c = 5 + b
\n" ); document.write( "From \"you can buy both cartridge for a total of $43.50\" we get:
\n" ); document.write( "c + b = 43.50
\n" ); document.write( "There are many ways to solve such a system. Since the first equation is already solved for c, we can easily use the Substitution Method. Using the expression from the first equation we can substitute for c in the second equation:
\n" ); document.write( "(5 + b) + b = 43.50
\n" ); document.write( "Now we solve for the remaining variable, b. First we simplify the left side:
\n" ); document.write( "5 + 2b = 43.50
\n" ); document.write( "Subtract 5:
\n" ); document.write( "2b = 38.50
\n" ); document.write( "Divide by 2:
\n" ); document.write( "b = 19.25
\n" ); document.write( "So a black ink cartridge costs $19.25. But we are asked for the price of a color cartridge. So we use this result and either of the original equations to find c:
\n" ); document.write( "c = (19.25) + 5
\n" ); document.write( "which simplifies to:
\n" ); document.write( "c = 24.25
\n" ); document.write( "So a color cartridge costs $24.25.
\n" ); document.write( "P.S. This problem could also have been solved using a single variable. Since we know what the combined price of the cartridges is, $43.50, we can use:
\n" ); document.write( "Let c = the price of a color cartridge.
\n" ); document.write( "Then
\n" ); document.write( "43.50 - c = the price of a black ink cartridge.
\n" ); document.write( "With one variable we only need one equation. From \"A color cartridge for xt-100 inkjet printer is $5 more than twice the price of a black ink cartridge.\" we get:
\n" ); document.write( "c = 5 + (43.50 - c)
\n" ); document.write( "Simplifying the right side:
\n" ); document.write( "c = 48.50 - c
\n" ); document.write( "Adding c:
\n" ); document.write( "2c = 48.50
\n" ); document.write( "Dividing by 2:
\n" ); document.write( "c = 24.25 \n" ); document.write( "