# simultaneous equations

A gas bill consists of a fixed charge (£F) and charge (g pence) for each unit used. Mrs Ali used 350 units and paid 30 pounds. mr hill used 450 units and paid £35. find the fixed charge and the charge per unit.

If we call our total cost T, then:T = F + g/100If we plug in the values we have then:(1) 30 = F + 3.5g(2) 35 = F + 4.5gIf we do (2) - (1) we get:35 - 30 = F - F + 4.5g - 3.5g5 = gIf we then return to (1) with the knowledge that g = 5:30 = F + 3.5*530 = F + 17.5F = 12.5Thus the fixed charge is £12.5 and the charge per unit is 5p.
vandanparmar
01 September 2014
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vandanparmar
02 September 2014
100F + 350g = 3000(-)  100F + 450g = 3500-100g = -500g = 5 pence per unitAlso, 100F + 350 x 5 = 3000100F = 3000 - 1750100F = 1250F = 12.50 pounds
arvind14
16 September 2014
When ever solving simultaneous equations remember that there should be a common variable.In this case we have to find Fixed charge 'F'TOTAL AMOUNT PAID=FIXED CHARGE+UNIT*CHARGE PER UNITSO IT BECOMES30=F+350g------eq(2)35=F+450g------eq(!)subtracting eq(2) from eq(1)5=100g and so g is 5/100=.05so30=F+350*.0530=F+17.530-17.5=FF=12.5 so the fixed charge is £12.5 and charge per unit is£.05
09:26 on 03/09/14
16 September 2014
a=fixed charge,d=charge per unitsolve these equations:1)  a+(349)*d=30                (350-1=349)2)a+449*d=35                     (450-1=449)
kabir
17 September 2014
xvariable + fixed = 30yvariable + fixed = 35100 extra units cost £5 so the price per unit is 5p.350x5p is 17.50450x5p is 22.50now 30-17.50 is 12.50       35- 22.50 is 12.50fixed charge 12.50
joannajane
14 October 2014
Let T = total paid = £30and in general we have that ** T = F + ug, Where u is the amount of units used.now we have two equations:for Mrs Ali T=30, u=350. so by equation above ** 30 = F + 350gfor Mr Hill T=35, u=450. so by the same equation ** 35 = F + 450gnow notice that Mr Hill has paid £5 more for 100 extra units. Hence 100g=£5.so divide £5 by 100 and we have g = 5p.Now we can use either equation to find the fixed charge.Take Mrs Ali: then work out the charge for the units used 350g = 350*5 = 1750p = £17.50.SO using ** £30 = F + £17.50rearrange to find F = 30 - 17.50 = 12.50.Can check this is correct by substituting in to Mr Hills bill. T = 12.50 + 450*0.05 = £35:)
djpurnell
15 October 2014
yes, David's method is correct
bhavesh
15 October 2014
The equation for the gas bill is: GB = F+g*U (being GB the gas bill and U the units of gas used). For Mrs Ali, the equation is: 30 = F+350*gFor Mr Hill: 35 = F+450*gIf you subtract the first equation by the second one, you get: 30-35 = F-F+350g-450gThis will give you: -5 = 0 - 100gWhich is the same as 5 = 100gWe make g the subject and we obtain: g = 0.05 pounds, which is equal to 5p
Jordi C.
19 October 2014
This question has been answered already and joannajane has broken it down in detail. I will add a few comments.Be careful with the units. Depending on how you proceed you can end up with g = 0.05 or g = 5. Make sure you interpret your numerical answers correctly with respect to the question: £0.05 = 5p.In my opinion since they say that g is in pence I would take account of this from the start with the equations:                      F + 350 × (g ÷ 100) = 30                         Equation 1                      F + 450 × (g ÷ 100) = 45                         Equation 2The brackets are unnecessary for order of operations but do make things clearer (converting from pence to pounds). Now all the terms are consistent and expressed in £. Solving will give you an answer for g of 5 which is of course 5 pence. F will be 17.5 which is £17.50
brendan_h
20 October 2014
it is simplef+350 g =30                  ----1f+450 g = 35                 -----2now we can subtract equation 1 from equation 2 and get the value of g.100 g = 5 and g=.05we can put the value of 'g' in any equation and get the value of  'f'. i.e. 12.5
bhatt
24 October 2014