Question

I went to the grocery store the other day and there were no price tags on anything! I bought 3 loaves of bread and 1 milk jug and when the cashier scanned it, the total was $9. Then I saw the person behind me bought 1 loaf of bread and 2 milk jugs. Her total was $5.50. I walked out: how much does one loaf of bread cost?

Answer 1

To solve this problem, set up and solve a system of equations. The variables b and m will represent a bread loaf and milk jug, respectively:


`\left \{ {{3b + m = 9} \atop {b + 2m =5.5}} \right.`

I would solve using substitution. Take one of the equations and set it equal to one of the variables, for example:


`3b + m =9 \\ m = 9 -3b`

Now, plug this into the other equation for m and solve for b:


`b + 2m =5.5 \\ b + 2(9-3b)= 5.5 \\ b + 18 - 6b = 5.5 \\ -5b + 18 = 5.5 \\ -5b = -12.5 \\ b = 2.5`

We now know that a loaf of bread costs $2.50. Plug this value in for b in the first equation and solve for m:


`3b + m = 9 \\ 3(2.5) + m = 9 \\ 7.5+m = 9 \\ m = 1.5`

One jug of milk costs $1.50 and one loaf of bread costs $2.50.