At a bio-tech research facility, the ratio of male to female scientists is initially 5 : 3… — GMAT

At a bio-tech research facility, the ratio of male to female scientists is initially $5 : 3$ . After $4$ female scientists leave and $12$ male scientists join the facility, the ratio of male to female scientists becomes $4 : 1$ . If a group of $N$ additional female scientists subsequently joins the facility, changing the ratio of male to female scientists to $8 : 5$ , what is the value of $N$ ?

Cevap: 12

Cevap

The value of

N

is 12.

By setting up ratio equations stage-by-stage using multiplier

k

, we determine that

k = 4

, yielding 32 male and 8 female scientists after the first change. Solving

\frac{32}{8+N} = \frac{8}{5}

yields

N = 12

Adım Adım Çözüm

Define initial variables using a common ratio multiplier

k

Male scientists =

5k

, Female scientists =

3k

Ratios preserve proportionality through a constant multiplier.

Formulate and solve the equation for the first population adjustment.

\frac{5k + 12}{3k - 4} = 4 \implies 5k + 12 = 12k - 16 \implies 7k = 28 \implies k = 4

Adding 12 males and removing 4 females sets the new ratio to

4 : 1

Determine the exact number of male and female scientists at the facility after the first adjustment.

Male scientists =

5(4) + 12 = 32

; Female scientists =

3(4) - 4 = 8

Substitute

k = 4

back into the adjusted quantity expressions.

Formulate and solve the equation for the second population adjustment involving

N

\frac{32}{8 + N} = \frac{8}{5} \implies 8(8 + N) = 160 \implies 64 + 8N = 160 \implies 8N = 96 \implies N = 12

The number of male scientists remains 32 while female scientists increase by

N

to achieve an

8 : 5

ratio.

Anahtar Kavram

Multi-step ratio manipulation and algebraic modeling

Tahmini Süre:2m 0s

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