contestada

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?

Respuesta :

Answer:

Chips are $0.80 a bag

A bottle of water is $1.60

A gallon of milk costs $3.80

Step-by-step explanation:

Ver imagen jesscmheasley
semsee45

Answer:

$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.

Step-by-step 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:

[tex]\begin{cases}3x+4y+7z=23.40\\y=2z\\x=y+2.20\end{cases}[/tex]

Rearrange the second equation to make z the subject:

[tex]\implies z=0.5y[/tex]

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

[tex]\implies 3(y+2.20)+4y+7\left(0.5y\right)=23.40[/tex]

[tex]\implies 3y+6.6+4y+3.5y=23.4[/tex]

[tex]\implies 10.5y+6.6=23.4[/tex]

[tex]\implies 10.5y=16.8[/tex]

[tex]\implies y=1.60[/tex]

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

[tex]\implies x=1.60+2.20[/tex]

[tex]\implies x=3.80[/tex]

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

[tex]\implies 1.60=2(z)[/tex]

[tex]\implies z=0.80[/tex]

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.

Otras preguntas