By what percent will the product of two numbers decrease if one of them is decreased by 25%, and the other is decreased by 50%?

Question

contestada

Respuesta :

rvkacademic rvkacademic · Answer 1 · 2024-01-16T13:37:26+01:00

Answer:

[tex]62.5\%[/tex]

Step-by-step explanation:

Let x be the first number and y be the second number

If x is decreased by 25%, the new value of x will be 75% (100-25) of the current value

75% in decimal = 75/100 = 0.75
So new value of x = 0.75x

If y is decreased by 50%, the new value of y will be 50% (100-50) of the current value

50% in decimal = 50/100 = 0.50
So new value of x = 0.5x

The current product = xy

New product of the two numbers after decrease = (0.75x) · (0.50x)
= 0.375xy

The percentage decrease in the product is given by:
(original product - new product)/Original product × 100

This works out to
[tex]\dfrac{xy - 0.375xy}{xy} \times 100\\\\= \dfrac{0.625xy}{xy} \times 100\\\\= 0.625 \times 100\\= 62.5 \%[/tex]

ayenoe13 ayenoe13 · Answer 2 · 2024-01-16T13:38:43+01:00

Answer: 62.5%.

Step-by-step explanation:

Start with two numbers, let’s call them X and Y. The original product is written as: (X \cdot Y).

Decrease X by 25%:

The new value of X (denoted as X’) is calculated as: (X’ = X - 0.25 \cdot X = 0.75 \cdot X).

Decrease Y by 50%:

The new value of Y (denoted as Y’) is calculated as: (Y’ = Y - 0.5 \cdot Y = 0.5 \cdot Y).

The new product will be: [X’ \cdot Y’ = (0.75 \cdot X) \cdot (0.5 \cdot Y) = 0.375 \cdot X \cdot Y]

The new product is 37.5% of the original one. Therefore, the product decreases by 62.5%.