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Question 875833: leela sold her car seat covers at a profit of 7%. if she had sold it for $4.25 more, she would have got 10% profit. how much did leela sell her seat covers for?
With working out please.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! we let s = sale price of the item and c = cost of the item and p = profit of the item.
at 7% profit, our first equation becomes:
p = s - c
since profit is equal to 7% of the cost, we also get:
p = .07*c
when we replace p with it's equivalent expression of .07*c, our equation becomes:
.07*c = s - c
if we solve for s, we will get:
s = 1.07*c ***** see note 1 at the bottom on how to derive this.
our second equation is:
p = s + 4.25 - c
since p is also equal to .10*c in this equation, then this equation becomes:
.10*c = s + 4.25 - c
if we solve for s, we will get:
s = 1.10*c - 4.25 ***** see note 2 at the bottom on how to derive this.
we now have two equations that are both equal to s.
s is the original selling price.
the equations are:
s = 1.07*c
s = 1.10*c - 4.25
since s = 1.07*c in the first equation, we can replace s with its equivalent expression of 1.07*c in the second equation to get:
1.07*c = 1.10*c - 4.25
solve for c in this equation to get:
c = 4.25 / .03 ***** see note 3 at the bottom on how to derive this.
solve for c to get:
c = 141.66667 rounded to 5 decimal places.
since c is equal to the cost of the item, we now know what the cost is and we can proceed to solve the rest of the problem.
our first equation was .07*c = s - c
we solved for s to get 1.07*c = s ***** see note 1 at the bottom on how this was derived.
since c = 141.66667, we can solve for s to get:
s = 1.07*141.66667 which is equal to 151.583337 rounded to 5 decimal places.
if we add 4.25 to this, we will get a sale price of 155.83337 rounded to 5 decimal places.
151.583337 represents the original sale price at 7% profit.
155.83337 represents the new sale price after we add 4.25 to the original sale price.
p = s - c with the new sale price and the original cost becomes:
p = 155.83337 - 141.66667 = 14.1667
that's our new profit after we added 4.25 to the original sale price.
rate of profit = p / c = 14.1667 / 141.66667 = .10000 rounded to 5 decimal places.
that's a 10% profit using the new sale price, so we solved the problem correctly.
the answer to the question is:
leela sold her seat covers for $151.58 rounded to 2 decimal places.
That's the selling price at 7% profit.
notes are below:
***** note 1
start with:
.07*c = s - c
add c to both sides of this equation to get:
c + .07*c = s
factor out the c on the left side of this equation to get:
(1 + .07)*c = s
simplify to get:
1.07*c = s
that's the same as:
s = 1.07*c
***** note 2
start with:
.10*c = s + 4.25 - c
add c to both sides of this equation and subtract 4.25 from both sides of this equation to get:
c + .10*c - 4.25 = s
factor out the c on the left side of the equation to get:
(1 + .07)*c - 4.25 = s
simplify to get:
1.10*c - 4.25 = s
that's the same as:
s = 1.10*c - 4.25
***** note 3
start with:
1.07*c = 1.10*c - 4.25
subtract 1.07*c from both sides of this equation and add 4.25 to both sides of this equation to get:
4.25 = 1.10*c - 1.07*c
factor out the c on the right side of this equation to get:
4.25 = (1.10-1.07)*c
simplify to get:
4.25 = .03*c
divide both sides of this equation by .03 to get:
4.25/.03 = c
that's the same as:
c = 4.25 / .03
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