By what percent will the product of two numbers increase if one of them is increased by 50%, and the other is decreased by 20%?
(a*1.50)(b*0.80) = (ab)(1.20)
so, the product increased by 20%
To find the percentage increase in the product of two numbers, we will follow these steps:
Step 1: Calculate the new values of both numbers after the percentage changes.
Step 2: Calculate the product of the new values.
Step 3: Find the percentage increase in the product compared to the original product.
Let's assume the original numbers are x and y.
Step 1: Calculate the new values after the percentage changes.
If one number is increased by 50%, we can calculate it as:
New value of x = x + 0.5x = 1.5x
If another number is decreased by 20%, we can calculate it as:
New value of y = y - 0.2y = 0.8y
Step 2: Calculate the product of the new values.
Product of the new values = (1.5x) * (0.8y) = 1.2xy
Step 3: Find the percentage increase in the product compared to the original product.
To find the percentage increase, we need to compare the difference between the new and original product to the original product:
Percentage increase = ((New product - Original product) / Original product) * 100
Original product = xy
Let's substitute the values:
Percentage increase = ((1.2xy - xy) / xy) * 100
= (0.2xy / xy) * 100
= 0.2 * 100
= 20%
Therefore, the product of two numbers will increase by 20% if one of them is increased by 50%, and the other is decreased by 20%.