SOLUTION: Question: A heating and ventilation engineer purchases four 1m radiators and three 1.5m radiators at a cost of £159 for a project. In addition he purchases five 1m radiators and tw

Question 176170: Question: A heating and ventilation engineer purchases four 1m radiators and three 1.5m radiators at a cost of £159 for a project. In addition he purchases five 1m radiators and two 1.5m radiators at a cost of £134. Determine the cost of both types of radiator.
Found 2 solutions by EMStelley, Mathtut:
Answer by EMStelley(187) (Show Source):
You can put this solution on YOUR website!
First, let's declare some variables:
x: cost of 1m radiator
y: cost of 1.5m radiator
Then, the first sentence tell us that
and the second tells us

Let's use the addition method to solve. I will multiply the first equation by 5, and the second equation by -4:

Now we add the two together:

So the 1.5m radiator costs £37. 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:

So the 1m radiator costs £12.

Answer by Mathtut(3670) (Show Source):
You can put this solution on YOUR website!
lets call the cost of 1m and 1.5m radiators, r and s , respectively
:
4r+3s=159.....eq 1
5r+2s=134.....eq 2
:
multiply eq 1 by 2 and eq 2 by -3
:
::8r+6s=318....eq 1 revised
-15r-6s=-402....eq 2 revised
:
add the two equations together. as you can observe the s terms are eliminated because 6s-6s=0. We are left with 8r-15r=318-402.
:
-7r=-84
:
per 1m radiator
:
now plug the value of r just found into any of the equations. I choose eq 1
:
4(12)+3s=159--->3s=111
:
per 1.5m radiator