Posted: June 26th, 2022

MATH 1030 Business Mathematics

Question:

The following problems require you to define your unknowns and create an equation that is appropriate for the situation. Finally, solve the equation.

It may be useful to list all the “knowns” as well as to write a sentence about the situation. However, you don’t need to do this to get full credit.

Boater’s Paradise was able to sell five more boats at a recent boat show than Pelican Marine.

How many boats were sold by each company if they sold 33 together?

Cupcake Cafe earns 4 1/2 times more revenue from muffins than doughnuts.

How much revenue did each bakery make if total sales were $44,000 in May?

Ethan Hunt, the notoriously smart IMF, can capture a terrorist in ten working days.

Luther Stickell, a member of the same group, can capture the terrorist in just eleven days.

How many days can it take to capture the terrorist if you work together?

Answer:

Let B be the number of boats that were sold by Boater Paradise, and P the number of boats that were sold by Pelican Marin.

This information can be represented by the equation, as 33 total boats were sold.

Given that Boater Paradise sold five more boats than Pelican Marine’s, we can express B in terms P.

This equation can be substituted for the above.

Add 5 to each side of the equation.

Divide both sides by 2 to get the following:

Thus, P can be obtained as a value

Substituting B in P gives B the same value

Boater Paradise sold 19 boats, while Pelican Marine sold 14.

Let X be revenue from cupcake cafes on doughnuts, and Y the revenue from muffin shops.

The total revenue is 44000, hence the equation.

We have because revenue from cupcakes is 4 1/2x more than on muffins.

This can be substituted in the equation.

To solve the equation, multiply both sides of equation.

We get x by solving for it.

Accordingly, the revenue from cupcake cafes selling doughnuts is 36000 and that from muffins is 8000.

Ethan Hunt captures the terrorist in 10 days, which means that he completes the task of catching him in one day.

Luther Stickell captures the terrorist in 11 days, which means that he completes the task of capturing the terrorist in one day.

They can work together to complete the task in one day. This means they can catch the terrorist in days, which is equivalent of days.