help with math?

Question

someone please help me with these math problems on percentages.
1) By giving a discount of 30%, a trader makes a profit of 20%. If the trader had given a discount of $400, he would have incurred a loss of 20%. Find the marked price(price before discount) of the article.
2) A bag contains balls of 3 different colors-red,blue and green. The number of blue balls is 12.5% lesser than the number of red balls and 40% more than the number of green balls. By what percent is the sum of the blue and green balls less than the sum of the red and blue balls?

I want the explanation if possible.. just the answer wont help.
Thanks in advance.

Answer 1

#1) Let P = the price before discount, and
let C = trader's cost

70%P = 120%C

P - 400 = 80%C

Those are your two equations, let's simplify them and then solve:

0.7 P = 1.2 C
7P = 12C
I'm going to write this as C = 7/12 P, so that we can substitute.

P - 400 = 0.8 C, let's substitute for that C

P - 400 = 4/5 (7/12) P

P - 400 = 7/15 P

P - 7/15 P = 400

8/15 P = 400

P = 750

The original price is $750. Check it with the words!

Answer 2

w is the wholesale price; what the trader paid for the item.
r is the retail price; the price marked on the sticker.
A 30% discount means the trader was paid r-0.30r = 0.70r.
A 20% profit means the trader was paid w+0.20w = 1.20w.
A 20% loss means the trader was paid w-0.20w = 0.80w.

"By giving a discount of 30%, a trader makes a profit of 20%":
0.70r = 1.20w

"If the trader had given a discount of $400, he would have incurred a loss of 20%":
r-400 = 0.80w
Multiply this by 1.5 to match the preceding equation:
1.5(r-400) = 1.20w
so
0.70r = 1.5(r-400)
0.70r = 1.5r - 600
0.8r = 600
r = 750
You are not asked to solve for w.
======================
Let r, b, and g be the number of red, blue, and green balls, respectively.

"blue is 12.5% less than red":
b = r - 0.125r = 0.875r
r = b/0.875


"blue is 40% more than green":
b = g + 0.40g = 1.40g
g = b/1.40


"By what percent is the sum of the blue and green balls less than the sum of the red and blue balls?"
Percentages are just fractions that compare one number to another. In this question:
the sum of red and blue is the basis of comparison. BASIS of comparison...think "base"...think "low"...think "denominator". The denominator of this percentage will be (r+b).

what you're comparing to the basis is the difference between sum of blue and green and sum of red and blue. The numerator of this percentage will be (r+b) - (b+g).

The answer to the question is
[(r+b) - (b+g)]/(r+b)
where
r+b = b/0.875 + b =
= b/0.875 + 0.875b/b
= (b+0.875b)/0.875
= b(1.875/0.875)
and
b+g = b + b/1.40
= 1.40b/1.40 + b/1.40
= (1.40b + b)/1.40
= b(2.40/1.40)

I leave the hairy calculations to you. Somehow it reduces to a number with only one decimal digit. Remember to express it as a percentage.

Answer 3

Let x = amount trader paid for object
So .2x = profit
.3x = discount
So 1.5x = final sell price
1.5x -400 = .8x
.7x = 400 --> x = $571.43
So 1.5*571.43= $857.15 price before discount

B = .875R
B= 1.4G
B+G=B+B/1.4
B+R = B+B/.875
Difference of sums is B/.875-B/1.4 = 2B/7
So (2B/7) / 15B/7 = 2/15 = 13.33%