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(5) The PC paint company makes paint using two kinds of paint.

Paint A is 60% acrylic, 10% latex and the rest is water. It costs $50 per liter.
Paint B is 10% acrylic, 50% latex and the rest is water. It costs 820 per liter.
(a) If 10 liters of paint A is mixed with 40 liters of paint B, what percentage is acrylic ?
Give the answer as a number eg 6.4 or 17
%
(b) If 10 liters of paint A is mixed with (50-10z) liters of paint B, how many liters of acrylic are in
this mixture? The answer is pr+q where p and q are integers where
A
(c) A customer wants 50 liters of paint that is 30% acyrlic. How many liters of each paint are used?
The answers are integers. (hint: check your answers gives right amount of acrylic)
number of liters of paint A needed is
number of liters of paint B needed is
(d) PC sells the paint to the customer for $3000. How much profit does PC make the answer is an
integer,
IS
(e) How many liters of water is in the paint used in part (e)"
Give answ as a decimal number like 3.7
Liters

1 Answer

5 votes

a) If 10 liters of paint A is mixed with 40 liters of paint B, the percentage of acrylic is 20%.

b) If 10 liters of paint A is mixed with (50-10z) liters of paint B, there are (11 - z) liters of acrylic in the mixture.

c) To make 50 liters of paint that is 30% acrylic, the customer should use 20 liters of Paint A and 30 liters of Paint B.

d) If PC sells the paint to the customer for $3,000, PC makes a profit of $1,400.

e) The total amount of water in the paint mixture is 19 liters.

The percentage of acrylic in the mixture = The total amount of acrylic in each type of paint divided by the total volume of the mixture.

In 10 liters of Paint A, the amount of acrylic is 60% of 10 liters, which = 6 liters (10 x 60%).

In 40 liters of Paint B, the amount of acrylic is 10% of 40 liters, which = 4 liters (40 x 10%).

Thus, the total amount of acrylic in the mixture is 6 liters (from Paint A) + 4 liters (from Paint B) = 10 liters.

The total volume of the mixture is 10 liters (of Paint A) + 40 liters (of Paint B) = 50 liters.

Therefore, the percentage of acrylic in the mixture is (10 liters / 50 liters) * 100% = 20%.

Thus, we can conclude that the mixture is 20% acrylic.

b) Let’s calculate the amount of acrylic in the mixture:

In 10 liters of Paint A, the amount of acrylic is 60% of 10 liters, which is 6 liters.

In ((50 - 10z)) liters of Paint B, the amount of acrylic is 10% of ((50 - 10z)) liters, which is (0.1 \times (50 - 10z)) liters.

So, the total amount of acrylic in the mixture is the sum of the acrylic from Paint A and Paint B:

Total Acrylic = 6 + 0.1 × (50−10z) = 6 + 5 − z

Simplifying this gives:

Total Acrylic = 11−z liters

Thus, there are (11 - z) liters of acrylic in the mixture.

c) Let the amount of Paint A used = x liters

Let the amount of Paint B used = y liters.

The total amount of paint used is 50 liters, so (x + y = 50).

The total amount of acrylic in the mixture is 30% of 50 liters, which is 15 liters. Since Paint A is 60% acrylic and Paint B is 10% acrylic, we have (0.6x + 0.1y = 15).

We have formed a system of two equations with two unknowns and can solve this system to find the values of (x) and (y).

Multiplying the second equation by 10 gives us (6x + y = 150). Subtracting the first equation from this gives us (5x = 100), so (x = 20).

Substituting (x = 20) into the first equation gives us (20 + y = 50), so (y = 30).

Thus, to make 50 liters of paint that is 30% acrylic, the customer should use 20 liters of Paint A and 30 liters of Paint B.

d) Computation of Profit:

The total revenue = $3,000

From the previous parts of the problem, we know that 20 liters of Paint A and 30 liters of Paint B are used. Given that Paint A costs $50 per liter and Paint B costs $20 per liter, we can calculate the total cost:

Cost of Paint A = 20 liters * $50/liter = $1,000

Cost of Paint B = 30 liters * $20/liter = $600

So, the total cost is $1000 (for Paint A) + $600 (for Paint B) = $1,600.

The profit:

Profit = Total Revenue - Total Cost

= $3000 - $1600 = $1400.

So, PC makes a profit of $1400.

e) In part (a), we mixed 10 liters of Paint A and 40 liters of Paint B.

Paint A is 60% acrylic, 10% latex, and the rest is water. So, in 10 liters of Paint A, there is 30% of water, which is 3 liters.

Paint B is 10% acrylic, 50% latex, and the rest is water. So, in 40 liters of Paint B, there is 40% of water, which is 16 liters.

Thus, the total amount of water in the paint mixture is 3 liters (from Paint A) + 16 liters (from Paint B) = 19 liters.

Complete Question:

e) How many liters of water is in the paint used in part (a)?

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