Question

math help ss below

Answer 1

@AZ

Answer 2

oh ok

Answer 3

So he makes a profit of x% of his costs

that means if costs was c

his profits are
x% * c

and if he reduces his costs by 8%
then his costs are 0.92*c

and the profit is increased by (x+10)%

Answer 4

hmmm we need to make it into equations so that way we can solve these two situations for 'x'

Answer 5

oh
how would we do that?
im very confused lol

Answer 6

okay so let's go back to some basics

selling price - cost price = profit

so if you're selling something for $10 but it only costs $3 to make it, then your profit is $7

so originally, let's say that the cost price was 100
we had a profit of x% so profit is x
the selling price is S

now, we reduce the cost price by 8% so it's 92
the profit increased by (x+10)% so the profit is x+10
and the selling price, S, remained the same

so can you write the two equations now?

Answer 7

um
s-100=x
s-92=x+10

Answer 8

okay actually that's not right uhh

Answer 9

oh what was wrong?

Answer 10

my method ;-;

Answer 11

so maybe we need to use the percentages

% profit = (S - C)/C * 100

(S is selling price and C is the cost)

so originally

x/100 = (S - C)/C * 100

and then cost is reduced by 8% and profit becomes (x+10)

(x+10)/100 = (S - 0.92C)/ (0.92C) * 100

Answer 12

that should get us to the write answer

Answer 13

ok i see that
how should cancel everything out tho?

Answer 14

let's simplify it

and I made a slight error, once we write x/100 we shouldn't have that *100 on the right side
because we converted the % into a fraction on the left side so there's no need to be multiplying by 100 on the right side

x/100 = (S - C)/C

x/100 = S/C - 1

and the second equation is
(x+10)/100 = S/(0.92C) - 1

Answer 15

does that make sense so far?

I basically simplified the fractions

now for the first equation, if you solve it for S/C
you can then plug that into the second equation

Answer 16

wait what do u mean by solve it for s/c?

Answer 17

x/100 = S/C - 1

just add 1 to both sides and you'll have the equation S/C = something

and you can then plug this into

(x+10)/100 = S/(0.92C) - 1

since

\(\dfrac{x+10}{100} = \dfrac{1}{0.92}\left(\dfrac{S}{C}\right) - 1\)

Answer 18

I hope it's making sense

Answer 19

so SC=x/100+1
then i plug it in and do the math?

Answer 20

Yup!

Answer 21

it might be easier if you simplify that back into (x+100)/100

and then you can multiply it with 1/0.92

and then the -1 just make it have the same denominator and then subtract

Answer 22

so i used wolfram and then x is around 15?

Answer 23

yes :)

Answer 24

I mean idk if you would say it's around 15. It is 15