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(208) (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
RELATED QUESTIONS
An electric radiator which is an ordinary constant resistor emits a heating power of 1.2... (answered by rfadrogane,Alan3354)
hello we had a chap doing pre delivery inspections on diesel generators refering to the (answered by Fombitz)
An electric heating system costs $5000 to install, with yearly operating cost of $1100. A (answered by macston)
According to the American Society of Heating, Refrigerating and Air-Conditioning... (answered by CPhill)
Heat and electricity costs together cost a company Rs. 10,800 for the month of February.... (answered by josgarithmetic)
A British thermal unit (Btu) is the amount of heat needed to raise the temperature of 1... (answered by greenestamps)
Alexandra purchases two doughnuts and three cookies at a doughnut shop and is charged... (answered by solver91311)
Alexandra purchases two doughnuts and three cookies at a doughnut shop and is charged... (answered by josgarithmetic)
Write and solve an equation to find three consecutive integers with a sum of... (answered by saifoo.khan)