By what percentage must the sales grow to maintain the same profit?

[chawki]

Homework Statement

The price of a product is reduced by 12%.

Homework Equations

By what percentage must the sales grow, if the profit should he the same ?

The Attempt at a Solution

let's assume the original price is P, and the number sold was x, then the original revenue is P*x.

reduction of 12% means that the new price is 0.88*P, Thus the new revenue is 0.88*P*x

 

[Mark44]

Homework Statement

The price of a product is reduced by 12%.

Homework Equations

By what percentage must the sales grow, if the profit should he the same ?

The Attempt at a Solution

let's assume the original price is P, and the number sold was x, then the original revenue is P*x.

reduction of 12% means that the new price is 0.88*P, Thus the new revenue is 0.88*P*x

That would be the revenue if the number of sales didn't change. The problem asks you to find the percent increase in sales that must occur so that the profit (really the revenue) will stay the same.

Write an equation that sets the old revenue, Px, equal to the revenue at the lower price but with increased sales.

 

[chawki]

ahh ok

P*x = 0.88*P*y
y = 1.1363x

 

[Mark44]

That looks fine, but you still need to answer the question - By what percentage must the sales grow, if the profit should he the same ?

 

[chawki]

yeah i think it's 13.63%

 

[chawki]

right?

 

[Mark44]

Rounded to 2 decimal places it would be 13.64%.