Question

Arah went to the grocery store and bought 4 loaves of bread and 1 gallon of milk for $12. The next week, Sarah bought 2 loaves of bread and 3 gallons of milk for $13.50. Which system of equations below can be used to determine the cost of one loaf of bread (b) and one gallon of milk (m)?

Answer 1

Here, b represents one loaf of bread and m represents the one gallon of milk.

As per the statement:

Arah went to the grocery store and bought 4 loaves of bread and 1 gallon of milk for $12.

⇒
`4b+m = 12`

It is also given that the next week, Sarah bought 2 loaves of bread and 3 gallons of milk for $13.50.

⇒
`2b+3m = 13.50`

Then; system of equation :

`4b+m = 12` .....[1]

`2b+3m = 13.50` .....[2]

Solve for b and m using above system of equations.

Multiply equation [2] by 2 we get;

`4b+6m = 27` .....[3]

Subtract equation [1] from [3] we get;

`4b+6m - 4b -m= 27-12`

Combine like terms;

`5m= 15`

Divide both sides by 5 we get;

m = $3

Substitute the value of m in equation [1] we get;

`4b+3 = 12`

Subtract 3 from both sides we get;

`4b=9`

Divide both sides by 4 we get;

b = $2.25

Therefore, cost of one loaf of bread (b) and one gallon of milk (m) are:

$2.25 ad $3