vinay1983 wrote:Four friends Laura, Nancy, James and Simon buy some pencils, pens and erasers from a shop. Laura buys 5 pencils, 6 pens, and 1 eraser for $17.50. Nancy buts 3 pens, 3 pencils, and 2 erasers for $ 10. James buys 5 pens, 2 pencils, and 5 erasers for $14.50. How much will Simon have to pay if he buys 3 pens, 2 pencils, and 5 erasers?
Note: How often in the GMAT do such questions appear?
Can i have a generic way to solve such questions?
x = pencil
y = pen
e = eraser
17.5 = 5x + 6y + 1e________________(1)
10 = 3x + 3y + 2e _________________(2)
14.5 = 2x + 5y + 5e________________(3)
2*(1) - (2):
35 - 10 = 7x + 9y
25 = 7x + 9y_________________(4)
5*(1) - (3):
87.5-14.5 = 23x + 25y
73 = 23x + 25y_______________(5)
(4)*25 - (5)*9
625 - 657 = 175y - 207x
32 = 32x
x = 1
Substitute x in (4)
25 = 7 + 9y
9y = 18
y = 2
Substitute in x and y in (2):
10 = 3 + 6 + 2e
2e = 1
e = 1/2
Now, to buy 3 pens, 2 pencils and 5 erasers, Simon will have to pay
2x + 3y + 5e = 2 + 6 + 2.5
[spoiler]= $10.5[/spoiler]
Generic method:
1. Solve 2 equations to eliminate one variable.
2. Solve another 2 equatios to eliminate the same variable.
You have now reduced the problem to 2 equations with 2 unknowns.
3. Solve these two equations to get the 2 unknowns.
4. Substitute the unknowns in the original equation to get the third unknown.
I don't know of any other short cut. Suggestions are welcome.
Cheers
