1/15

35% → .35

quantity = q

35/100 q = .35q

But if q is increased by 35% the new amount is

q +.35q = (1 + .35) q

But if q is reduced by 35% the new amount is

q -.35q = (1-.35) q = .65q

Example:

Each unit cost you $200 to make. You want the profit to be 50% of the selling price. What should the price be?

$Let x= selling price$

cost is 200 Profit - x-200 } Profit=.50x

                                         x-200 = .50x

                                            .5x=200

                                             x=400

Inequalities in word problems

Word problems lead to inequalites when the stated goal is to ‘make profit” ( meaning profit is positive)

or the words “at most”, “at least”, “more”, “less” appear

Pay attention to inequality signs like >(equal to) and > For e

REVENUE= R(x)= 25x

Cost- ((x)= 100,000 +15x

Profit= P(x) = Revenue- Cost= 25x- (100000 +15x) = 40x- 100000

make a profit: profit > 0

10x- 100000 > 0 {Add 100000}

10x> 100000 { Divide by 10 }

x> 10000

Let x= # units sold → ((x)= 100,000 +15x } # units sold= (1-.1)x+ .9x

R(x)= 25x (.9x) = 22.5x

P9x) = 22.5x-(100000 +15x) =7.5x -100000