Given that G=ab, find the percentage increase in G when both a and b increase by 10%.
Answer:
The percentage increase in X is 21%.
Step-by-step explanation:
Given that X=ab ,find the percentage increase in X when both a and b increases by 10%.
Given: X=ab, a is increased by 10%, b is increased by 10%
Asked: The percentage increase in X
Solutions:
Change 10% into decimal and that is 0.10 or 0.1
If a is increased by 10% or 0.1, then it will become,
a + 0.1a
= 1a + 0.1a It is understood that a has a numerical coefficient of 1.
= 1.1a
If b is increased by 10% or 0.1, then it will become,
b +0.1b
= 1b + 0.1b It is understood that b has a numerical coefficient of 1.
= 1.1b
Using the given X = ab, when both a and b is increased by 10% or 0.1, then
X = (1.1a) (1.1b)
=1.21ab
In the given X = ab, ab as a numerical coefficient of 1. Thus,
1.21ab - ab
= 1.21ab - 1ab It is understood that ab has a numerical coefficient of 1.
= 0.21 Change into percent by moving the decimal point to the right (two decimal places) and add the percent sign.
= 21% is the percentage increase in X when both a and b increase by 10%
estimate any number for a and b
like, if a = 100
and b also equals 100
G will equal 100 * 100 G=10,000
since the percentage increase is 10% we add 10 to a and b
a=110 and b=110
so G will equal 110*110 which equals G=12,100
to find the percentage increase:
10,000 100%
(12100-10000)
2100 x
x=21%
G = ab
(1.1a)(1.1b) = 1.21 ab = 1.21G
G increases by 21%
To find the percentage increase in G when both a and b increase by 10%, we can start by understanding how G is calculated.
The equation given is G = ab, where G represents the value obtained by multiplying a and b.
Let's say the original values of a and b are a₀ and b₀, respectively. After increasing both a and b by 10%, the new values become:
New a = a₀ + 0.1a₀ = 1.1a₀
New b = b₀ + 0.1b₀ = 1.1b₀
Substituting these new values into the equation for G, we get:
New G = (1.1a₀)(1.1b₀) = 1.21a₀b₀
Now, let's calculate the percentage increase in G. The percentage increase is given by:
(Change in G / Original G) * 100
The change in G can be calculated by subtracting the original G from the new G:
Change in G = New G - Original G = 1.21a₀b₀ - ab = a₀b₀(1.21 - 1) = a₀b₀ * 0.21
Therefore, the percentage increase in G is:
(Change in G / Original G) * 100 = (a₀b₀ * 0.21 / ab) * 100
Since G = ab, the terms containing a₀b₀ cancel out, and we are left with:
Percentage increase in G = 0.21 * 100 = 21%
Hence, the percentage increase in G when both a and b increase by 10% is 21%.