Paul has $20,000 to invest. His intent is to earn 11% interest on his investment.

In the 8% option , $5,000 should be invested

In the 12% option, $15,000 should be invested

Step-by-step explanation:

Let’s start with the total return.

Since the total return expected is 11%, the amount expected to be returned will be;

11/100 * 20,000 = $2,200

Now, let the amount invested at 8% interest be $x while the amount invested at 12% interest be $y

Mathematically;

x + y = 20,000 ••••••(i)

Now let’s work with the interest part;

On the 8% part, amount of interest expected is 8/100 * x

on the 12% part, amount of interest expected is 12/100 * x

8% of $x + 12% of $y = 2,200

Writing this fully mathematically, we have;

(8/100 * x) + (12/100 * y) = 2,200

8x/100 + 12y/100 = 2,200

Multiply through by 100

8x + 12y = 220,000 ••••••(ii)

Now we have two equations to solve simultaneously;

x + y = 20,000

8x + 12y = 220,000

From i, x = 20,000-y

Substitute this into ii

8(20,000-y) + 12y = 220,000

160,000-8y + 12y = 220,000

4y = 220,000 - 160,000

4y = 60,000

y = 60,000/4

y = $15,000

x = 20,000 -y

x = 20,000 - 15,000

x = $5,000

The coefficient 3.99 represent the cost of one bottle of nail polish.

Step-by-step explanation:

Given:

The equation to represent the amount of money left after buying 'p' bottles of nail polish is given as:

The remaining amount with Itzel can be calculated as:

Remaining amount = Initial amount - Cost of 'p' bottles.

The above expression tells us two things:

1. Initial amount of money Itzel has was 25.

2. The cost of 'p' bottles of nail polish is .

Therefore, the cost of one bottle is calculated using the unitary method is given as:

Therefore, cost of 1 bottle of nail polish is 3.99. Hence, coefficient 3.99 represent the cost of one bottle of nail polish.