word problem

Question

Problem
Bhavik bought 3 liters of milk and 5 loaves of bread for a total of $11. A month later, he bought 4 liters of milk and 4 loaves of bread at the same prices, for a total of $10.
How much does a liter of milk cost, and how much does a loaf of bread cost?

Answer 1

Let m=liters of milk and let b=loaves of bread

 

Create an equation for each trip to the store:

3m + 5b = 11            

4m + 4b = 10

 

Solve for one of the variables so you can do substitution

4m + 4b = 10

      - 4b        -4b

4m = 10 - 4b

  /4     /4   /4

m = 2.5 - b

 

now substitute m=2.5-b  in the other equation 

3m + 5b = 11

3(2.5 - b) +5b = 11

7.5 - 3b + 5b = 11

7.5 + 2b = 11

-7.5          -7.5

     2b = 3.5

    /2      /2

     b =  1.75         bread costs $1.75

 

now use the cost of bread in either equation to solve for the cost of milk

4m + 4b = 10

4m + 4(1.75) = 11

4m + 7 = 11

      - 7   - 7

4m = 4

/4     /4

 m = 1           milk costs $1.00

 

Answer 2

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