Math word problem

Question

The cost of 2 loaves of bread and 1 case of milk is $35. The cost of 3 loaves of bread and 4 cases of milk is $69. What is the cost of 1 loaf of bread, and the cost of 1 case of milk? (Hint: use equations)

Answer 1

Step 1.  Translate the first sentence into one equation in two variables.  Using b for bread, and m for milk, we have:

 

2b +1m = $35.00

 

Step 2.  Translate the second sentence into a second equation in the same two variables.

 

3b + 4m = $69.00

 

Step 3.  Transform the first equation into a new equation by multiplying both sides by -4.

 

-8b -4m = -$140.00

 

Step 4.  Stack the two equations, and add them together.

 

 3b + 4m = $69.00

-8b - 4m = -$140.00

_________________

 

-5b =-$71.00

 

Step 5.  Solve for b by dividing both sides of the equation by -5.

 

b = $14.20

 

Step 6.  Solve for m by substituting the value of b in either equation.

 

2($14.20) + 1m = $35.00

 

Step 7.  Solve for m, by subtracting 28.40 from both sides.  

 

m = $6.60

 

Step 8.  Add the two variables.

 

1b + 1m = $14.20 + $6.60 = $20.80