Question

On a recent trip to the convenience store, you picked up 3 gallons of milk, 4 bottles of water, and 7 snack-size bags of

chips. Your total bill (before tax) was $23.40. If a bottle of water costs twice as much as a bag of chips, and a gallon of
milk costs $2.20 more than a bottle of water, how much does each item cost?

Answer 1

$3.80 = cost of one gallon of milk.

$1.60 = cost of one bottle of water.

$0.80 = cost of one snack-size bag of chips.

Explanation:

Define the variables:

• Let x = one gallon of milk.
• Let y = one bottle of water.
• Let z = one snack-size bag of chips.

Total items purchased:

• 3 gallons of milk.
• 4 bottles of water.
• 7 snack-size bags of chips.

Given information:

• Total bill (before tax) = $23.40.
• A bottle of water costs twice as much as a bag of chips.
• A gallon of milk costs $2.20 more than a bottle of water.

Create a system of equations with the given information:

`\begin{cases}3x+4y+7z=23.40\\y=2z\\x=y+2.20\end{cases}`

Rearrange the second equation to make z the subject:

`\implies z=0.5y`

Substitute the found expression for z and the third equation into the first equation and solve for y:

`\implies 3(y+2.20)+4y+7\left(0.5y\right)=23.40`

`\implies 3y+6.6+4y+3.5y=23.4`

`\implies 10.5y+6.6=23.4`

`\implies 10.5y=16.8`

`\implies y=1.60`

Substitute the found value of y into the third equation and solve for x:

`\implies x=1.60+2.20`

`\implies x=3.80`

Substitute the found value of y into the second equation and solve for z:

`\implies 1.60=2(z)`

`\implies z=0.80`

Conclusion:

• $3.80 = cost of one gallon of milk.
• $1.60 = cost of one bottle of water.
• $0.80 = cost of one snack-size bag of chips.

Answer 2

Chips are $0.80 a bag

A bottle of water is $1.60

A gallon of milk costs $3.80

Explanation: