To make purple paint we need to maintain a 3:2 ratio of red paint to blue paint .Red paint cost $20 a gallon and blue paint cost $25 a gallon .A coupon gives 10% discount on red paint and 20% discount on blue paint .If you have$500 for paint .what is the maximum amount of red and blue paint you can buy to make purple paint .

Question

To make purple paint we need to maintain a 3:2 ratio of red paint to blue paint .Red paint cost $20 a gallon and blue paint cost $25 a gallon .A coupon gives 10% discount on red paint and 20% discount on blue paint .If you have$500 for paint .what is the maximum amount of red and blue paint you can buy to make purple paint .

Answer 1

red (w/discount) ... $18 per gallon

blue (w/discount) ... $20 per gallon

(3 n * 18) + (2 n * 20) ≤ 500

54 n + 40 n ≤ 500 ... 94 n ≤ 500 ... n ≤ 5 15/47

3 n = 15 gal red ... 2 n = 10 gal blue

Answer 2

To determine the maximum amount of red and blue paint you can buy, let's start by calculating the budget for each type of paint:

1. Red Paint:
The cost of red paint per gallon is $20. With a 10% discount, the new price per gallon is: $20 - ($20 * 10%) = $18.

2. Blue Paint:
The cost of blue paint per gallon is $25. With a 20% discount, the new price per gallon is: $25 - ($25 * 20%) = $20.

Now, let's calculate the maximum amount of red and blue paint you can buy within your $500 budget:

1. Maximum Red Paint:
Since you have $500 in total, you can allocate a certain portion for red paint. Let's assume you can buy x gallons of red paint. With a price of $18 per gallon, the maximum amount of red paint you can buy is: x gallons * $18/gallon = $18x.

2. Maximum Blue Paint:
To maintain the 3:2 ratio of red to blue paint, the amount of blue paint needs to be 2/3 of the amount of red paint. So, the maximum amount of blue paint you can buy is: (2/3) * $18x = $12x.

Since the sum of the cost of red and blue paint cannot exceed $500, we can create the following equation:

$18x + $12x ≤ $500

Combining like terms:

$30x ≤ $500

Now, divide both sides by $30:

x ≤ $500 / $30
x ≤ 16.67

Therefore, you can buy a maximum of 16 gallons of red paint (since the value needs to be a whole number), and using the ratio, the maximum amount of blue paint you can buy is (2/3) * 16 = 10.67 gallons. Hence, you can buy 16 gallons of red paint and 10 gallons of blue paint to make purple paint while staying within your $500 budget.

Answer 3

To solve this problem, we need to find the maximum amount of red and blue paint we can buy within the given budget while maintaining the 3:2 ratio.

Let's assume we buy x gallons of red paint and y gallons of blue paint.

Given that red paint costs $20 per gallon and there is a 10% discount with the coupon, the effective cost per gallon of red paint is $20 - (10% of $20), which equals $20 - $2, or $18.

Similarly, blue paint costs $25 per gallon with a 20% discount, so the effective cost per gallon is $25 - (20% of $25), which equals $25 - $5, or $20.

Considering the 3:2 ratio, we can set up the following equation:

3x = 2y

Now let's calculate the maximum amount of paint we can purchase. We have a budget of $500, so the total cost must be less than or equal to $500:

18x + 20y ≤ 500

Now, let's find the values of x and y.

Using the equation 3x = 2y, we can substitute 2y for 3x in the budget equation:

18x + 20(3x/2) ≤ 500

18x + 30x ≤ 500

48x ≤ 500

x ≤ 500/48

x ≤ 10.42

We can't purchase less than a gallon of paint, so x = 10. This means we can buy 10 gallons of red paint.

Substituting x = 10 into the equation 3x = 2y:

3(10) = 2y

30 = 2y

y = 30/2

y = 15

So, we can buy a maximum of 10 gallons of red paint and 15 gallons of blue paint with a budget of $500 to maintain the 3:2 ratio and take advantage of the coupon discounts.