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# Ratios and Mixtures

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A dealer mixes three types of paints P, Q and R. Type P costs \$140 per litre, type Q costs \$160 per litre while type R costs \$256 per litre. The dealer mixed type P and Q in the ratio 5:3 to make a brand that sells at \$180 per litre.

(a) Calculate his percentage profit.

(b) The dealer made a new brand by mixing the three types of paint in the ratio P:Q = 5:3 and Q:R in the ratio 2:5. Determine the ratio P:Q:R in its simplest form.

(c) The selling price of the new brand if he has to make a 40% profit.

Jun 15, 2022

#1
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(a)   The new paint  has   8 equal parts

(5/8)  is paint P       and   (3/8)  is paint Q

So.....the   profit made is     180  -  (5/8)140  - (3/8)(160)  =    180  -  87.5 -  60  = \$32.50

% profit   =  profit / cost to produce  =   32.50 /  (87.5 + 60)  ≈   .22  ≈  22%

b)  P : Q =  5 : 3           Q : R   =  2 : 5

P  : Q  = 10 : 6       Q :  R =    6 : 15

So   P :  Q  :  R =   10 : 6 : 15

c)   Cost to produce one litre of the new mixture

We have  10 + 6 + 15 =   31 equal  parts

P= 10/31    Q =  6/31    R  =  15/31

(10/31)(140)  + (6/31)( 160)  + ( 15/31)( 256)  =   \$200

For a 40% profit it needs to sell at

Profit   / Cost to Produce =   .40

Profit  / 200 = .40

Profit  =  200 * .40  =  80

200 + 80    =  \$280   Jun 15, 2022
edited by CPhill  Jun 15, 2022
#2
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(a) P:5x Q:3x (P = Q = 5x : 3x = 5:3)

per profit = (180 (5x + 3x) - 140 (5x) - 160 (3x))/(140 (5x) + 160 (3x)) * 100%

= (1440x - 1180x)/1180x * 100%

= 0.220 * 100%

= 22% or 22.03%

(b) P:Q = 5:3

P = 10x, Q = 6x (P:Q = 10x : 6x = 5:3)

Q = R = 2:5

Q = 6x, R = 5(3)x = 15x

(Q : R = 6x : 15 = 6:15 = 2:5)

=> P = Q : R = 10x = 6x = 15x = 10 : 6 : 15

(c) selling price = y

40% = (y (10x + 6x + 15x) - 140 (10x) - 160 (6x) - 256 (15x))/(140 (10x) + 160 (6x) + 256 (15x))

=> 0.4 = (31 * y / 6200x)/6200x

0.4 = (31y - 6200)/6200 => 31y = 8680, y = \$280 per litre

Jun 15, 2022
edited by Slimesewer  Jun 15, 2022