a girl bought 1 sandwhich and 2 coke for 95pesos. a boy bought 2 sandwhiches and 1 coke for 85 pesos. how much is 1 sandwhich?

Question

The problem looks so easy but i wasnt able to answer it.

Answer 1

Let S=cost of a sandwich;     C = cost of a Cocke

 

Ask, can the coefficients of the term we want to eliminate (C) be made to add/subtract giving 0?

 

2S + 1C = 85       (boy's purchase)

 

4S + 2C = 170    (2*boy's purchase)

1S + 2C =   95     (girl's purchase)

-------------------

3S         =    75     (subtract equations to eliminate C)

      S = 25              (divide each side by 3)

Answer 2

Let x = cost of 1 sandwich

Let y = cost of 1 coke

 

 

Set equations using the variables and information given.  One equation for what the girl bought, and another for what the boy bought.

 

 

x + 2y = 95            eq1

2x + y = 85             eq2

 

 

Since we want to know the cost of 1 sandwich, we only need to solve for the variable x.  

 

Multiply eq2 by 2.  Keep eq1 as it is.

 

x + 2y = 95                 eq1

4x + 2y = 170              eq2

 

 

Subtract eq2 from eq1 to eliminate the y terms.

 

-3x = -75

 

x = 25

 

 

The cost of 1 sandwich is 25 pesos.