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

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