Explanation

 We are given:

To find $q$, divide both sides by 0.87:

Explanation

Let’s say you originally have $100, and the original price per unit is $1. You can buy:

Before price drop: $100 ÷ $1 = 100 units

A 60% price decrease means the new price is:

New price = $1 - 60% of $1 = $0.40

After price drop: $100 ÷ $0.40 = 250 units

So, the increase in quantity is:

250 - 100 = 150 units more, which is a 150% increase.

Explanation

Given:

xy = 35

x + y = 12

To find x² + y²:

(x + y)² = x² + 2xy + y²

144 = x² + 2(35) + y²

144 = x² + 70 + y²

x² + y² = 144 - 70

= 74

Explanation

Given:

Initial value = 80

Final value = 80

Percentage increase = ((Final - Initial) / Initial) × 100

= ((80 - 80) / 80) × 100

= (0 / 80) × 100

= 0%

Explanation

Given x + 1/x = 3

To find x³ + 1/x³:

(x + 1/x)³ = x³ + 3(x²)(1/x) + 3(x)(1/x)² + 1/x³

= x³ + 3x + 3/x + 1/x³

= x³ + 1/x³ + 3(x + 1/x)

(x + 1/x)³ = x³ + 1/x³ + 3(3)

27 = x³ + 1/x³ + 9

x³ + 1/x³ = 27 - 9

= 18