Translate each real-world situations into a multi-stepequation. Solve the equation, showing all steps to solve the equation. Thenwrite an explanation of the answer to the problem. Please write out the steps to solving each problem and write it like a word problem.

1. You and your friend are shopping for painting supplies.Your friend wants five bottles of paint and one set of paint brushes. You wantseven 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 oneset of paint brushes?

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

3. The formula to find the surface area of a sphere is totake the radius of the sphere and square it and multiply that amount by pi andthen multiply that by 4. This is written algebraically as S=4πr2, where S isthe surface area, r is the radius, and the value of π is 3.14. Rewrite the equationto solve for the radius of the sphere if you know the sphere’s surface area.Then estimate the radius of a sphere given a surface area of 500 meters^2.

Write two real-world problems that can be solved usingmulti-step equations that use fractions or decimals. Solve each equation,showing and explaining all your steps. Then write an explanation of the answerto the problem.