Respuesta :
Answer:
Percentage increase in consumption of apples by the family = 11.11%
Step-by-step explanation:
Let us assume that a family spends $100 on [tex]x[/tex] number of apples at the start.
Price of apples goes down by 10% which means [tex]x[/tex] apples would now cost $90.
For $90 the family can buy =[tex]x[/tex] apples
So for $1 the family can buy = [tex]\frac{x}{90}[/tex] apples
So for $100 the family can buy = [tex]\frac{x}{90}\times100 =\frac{100x}{90}=\frac{10x}{9}[/tex] apples
Increase in consumption =New consumption-Previous consumption= [tex] \frac{10x}{9}-x [/tex]
Taking LCD.
[tex]\frac{10x}{9}-\frac{9x}{9}=\frac{x}{9}[/tex] apples is the increase in consumption
Percentage increase in consumption= [tex]\frac{\ Increase\ in\ consumption}{Previous\ consumption}\times 100[/tex]
=[tex](\frac{x}{9}\div x)\times 100\\[/tex][tex]=(\frac{x}{9}\times\frac{1}{x})\times 100\\[/tex][tex]=\frac{1}{9}\times 100\\[/tex]
[tex]=11.11[/tex]%
Percentage increase in consumption of apples by the family = 11.11%
The family's apples consumption is increased by a percentage of 11%.
How much increases the percentage of apples bought?
Let's assume that the family spends N on apples, such that if the price of the apples is p, the number of apples bought is:
n = N/p.
If the price decreases by 10%, the new price is:
p' = 0.9*p
Then the new number of apples that the family can buy is:
n' = N/(0.9*p) = (1/0.9)*n = 1.11*n
So, the family can buy 1.11 times the number of apples that they could buy before the price decrease.
Then the percentage increase is:
P = (1.11 - 1)*100% = 11%
If you want to learn more about percentages, you can read:
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