Real world multi step equation

Question

1. You and your friend are shopping for painting supplies. Your friend wants five bottles of paint and one set of paint brushes. You want seven bottles of paint and two sets of paint brushes. Each bottle of paint costs $3.69. If you and your friend’s total cost is $51.69, what is the cost of one set of paint brushes?

 

 

 

2. In physics the mass energy equivalence is that the mass of a body is measured by its energy content. This may be written algebraically as E=mc2, where E is energy, m is mass, and c is the speed of light in a vacuum. Transform the equation so that it will be read as a solution for mass, m. Show all the steps.

 

 

Answer 1

1.  Let P = cost of a bottle of paint

     Let B = cost of a set of brushes

 

     Your friend buys 5P + B

                you buy  7P + 2B

 

     We know a bottle of paint costs $3.69

     and the total spent is $51.69

 

    5P + B + 7P + 2B = 51.69

    Combining like terms

    12P + 3B = 51.69

    Substitute 3.69 for P

    12(3.69) + 3B = 51.69

    44.28 + 3B = 51.69

    Subtract 44.28 from both sides

    3B = 51.69 - 44.28

    3B = 7.41

    Divide both sides by 3

    B = 7.41/3

    B = 2.47

 

A set of brushes costs $2.47

 

2.  E=mc²

    To solve the equation for m we need to divide both

    sides by what m is multiplied by... in other words

    divide both sides by c²

 

    E/c² = m

    Which is the same as

    m = E/c²

 

mass equals energy divided by the square of the speed of light in a vacuum