document.write( "Question 176170: Question: A heating and ventilation engineer purchases four 1m radiators and three 1.5m radiators at a cost of Ł159 for a project. In addition he purchases five 1m radiators and two 1.5m radiators at a cost of Ł134. Determine the cost of both types of radiator. \n" ); document.write( "

Algebra.Com's Answer #131260 by EMStelley(208) $\"\"$ $\"About$

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First, let's declare some variables:
\n" ); document.write( "x: cost of 1m radiator
\n" ); document.write( "y: cost of 1.5m radiator
\n" ); document.write( "Then, the first sentence tell us that
\n" ); document.write( " $\"4x%2B3y=159\"$ and the second tells us
\n" ); document.write( " $\"5x%2B2y=134\"$
\n" ); document.write( "Let's use the addition method to solve. I will multiply the first equation by 5, and the second equation by -4:
\n" ); document.write( " $\"20x%2B15y=795\"$
\n" ); document.write( " $\"-20x-8y=-536\"$
\n" ); document.write( "Now we add the two together:
\n" ); document.write( " $\"7y=259\"$
\n" ); document.write( " $\"y=37\"$
\n" ); document.write( "So the 1.5m radiator costs Ł37. Now, to find the cost of the 1m radiator, we substitute in this y value to either of the equations. I will use the first one for simplicity:
\n" ); document.write( " $\"4x%2B3%2837%29=159\"$
\n" ); document.write( " $\"4x%2B111=159\"$
\n" ); document.write( " $\"4x=48\"$
\n" ); document.write( " $\"x=12\"$
\n" ); document.write( "So the 1m radiator costs Ł12. \n" ); document.write( "

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