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leva [86]
3 years ago
10

Last year , there were 30 male members and 20 female members in a Chess Club . This year , the number of male members is decreas

ed by r% while the number of female members is increased by r% . If the number of male members is equal to that of female members this year , find the value of r .
Can anyone explain to me ?
Thks \(>∀<)/
Mathematics
1 answer:
LekaFEV [45]3 years ago
7 0

The r% of a quantity x is computed by dividing x in 100 parts, and considering r of such parts. So, the r% of the male is

30\times\cfrac{r}{100} = 0.3 r

and similarly, the r% of female is

20\times\cfrac{r}{100} = 0.2 r

The number of males decreased by this quantity, so now it is

30 - 0.3r

and the number of female increased by this quantity, so now it is

20+0.2r

we know that these two new counts are the same number, so we can build and solve the equality

30 - 0.3r = 20+0.2r

Subtract 20 and add 0.3r from both sides:

10 = 0.5r

Divide both sides by 0.5 to solve for r:

r = 20

Let's check the answer

The 20% of 30 is 30 \times \frac{20}{100} = 6, while the 20% of 20 is 4. So, we are stating that 30-6 = 20+4 which is true because both expressions evaluate to 24.

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