Question

the cost of 2 bottles of water and 3 bags of pretzels is $7.05. the cost of a bag of pretzels is $1.35. write a system of equations to represent this situation. solve and explain what the answer means

Answer 1

Answer:

• System of equations:

        1. 2w + 3p = 7.05

        2. p = 1.35

• Solution:

         w = 1.50

         p = 1.35

• The solution means that a bottle of water costs $1.50 and a bag of pretzels costs $1.35

Explanation

1) Translate the verbal language to algegraic language to create the equations which you can solve.

• Name the variables:

         w = cost of one bottle of water

         p = cost of one bag of pretzels

• First statement:

        the cost of 2 bottles of water: 2w

        the cost of 3 bags of pretzels: 3p

        the cost of 2 bottles of water and 3 bags of pretzels is $7.05:

                   2w + 3p = 7.05    Equation 1

• Second statement:

         the cost of a bag of pretzels is $ 1.35: p = 1.35    Equation 2

• System of equations:

        1. 2w + 3p = 7.05

        2. p = 1.35

2) Solve the system using substitution method: substitute p with 1.35 in the first equation:

• 2w + 3 (1.35) = 7.05

3) Steps to solve the equation:

• Simplify: 2w + 4.05 = 7.05

• Subtract 4.05 from both sides: 2w = 3

• Divide both sides by 2: w = 3/2 = 1.50

Answer: you have found the costs of both a bottle of water and a bag of pretzels, which, repectively, are $ 1.50 and $ 1.35