A system of equations, I must be setting it up wrong?

Question

For each of n people, Margie bought a hamburger and a soda at a restaurant. For each of n people, Paul bought 3 hamburgers and a soda at the same restaurant. If Margie spent a total of $5.40 and Paul spent a total of $12.60, how much did Paul spend just for hamburgers? (Assume that all hamburgers cost the same and all sodas cost the same.)
This is the way I set it up:
Quantity h + s = 5.4/3  = 1.8
Amount 3h + s = 1260

? · Accepted Answer

3h+s = 1260
h+s =    540
Subtracting,  2h = 1260-540 = 720
h = 720/2 = 360 cents = $3.60
Amount spent by Paun on hamburgers = 3s = 3*3.60 = $10.80

Douglas · Answer

The n multiplier is on both equations so it can be discarded.

h + s = $5.40 [1]
3h + s = $12.60 [2]

Subtract equation [1] from equation [2]:

2h = 7.20

h = $3.60

s = $5.40 - $3.60

s = $1.80

Check:

3(3.60) + 1.80 = $12.60

This checks.

grunfeld · Answer

H + S = 5.4 / n 
3H + S = 12.6 / n 

2H = (12.6 / n ) - ( 5.4 / n ) 
2H = 7.2 / n 
H = 3.6 / n 

S = 1.8 / n 


Paul spent 3( 3.6 / n ) = 10.80 / n  on hamburgers.

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A system of equations, I must be setting it up wrong?

3 Answers