2 muffins and a carton of milk cost $3.35. If 5 muffins and a carton of milk cost $5.60 what's the cost of 2 cartons of milk?

Question

A. $0.75

B. $1.50

C. $1.85

D. $3.70

Answer 1

This problem is a systems of equations problem. Each of the two sentences gives the information for one equation, and there are two pieces of information left out of each. This is another way of saying we have two equations and two unknowns.

 

If we take m to be the cost of a muffin and c to be the cost of a carton of milk, we can rewrite the first sentence as;

 

2m+c=3.35

 

The second sentence would then be;

 

5m+c=5.60

 

We can solve one of these equations to obtain an expression for one variable in terms of the other, then substitute that expression for its variable in the second expression, like so;

 

c=3.35-2m

 

5m+(3.35-2m)=5.60

 

I added the parenthesis to show what was substituted. They are unnecessary however. After this we combine like terms, etc.;

 

3m+3.35=5.60

 

3m=2.25

 

m=.75

 

We can plug this number back into the earlier expression for the cost of a carton of milk;

 

c=3.35-2(.75)

 

This is fairly trivial arithmetic at this point.

 

 

c=1.85

 

Another option is Elimination.

 

Use the same two equations, and multiply one entire equation by a constant that will enable one variable to be eliminated when the equations are added to one another.

 

Since we want c, we will attempt to eliminate m.

 

-2.5(2m+c)=3.35(-2.5)

-5m-2.5c=-8.375

 

Combine equations. Since both sides of the equation are equal, adding them this way is the same as adding the same number to both sides.

 

-5m-2.5c=-8.375

+(5m+c)        +5.60

 

-1.5c=-2.775

c=1.85

 

We have also verified our solution. Pick the method you like better.