At a research institute, the ratio of senior scientists to associate scientists to junior researchers was initially , respectively. During an organizational expansion, 8 new senior scientists were hired, and 4 junior researchers were promoted to associate scientists, while no other personnel changes occurred. If the new ratio of senior scientists to associate scientists became , what was the initial total number of researchers at the institute?
- A40
- B60
- C100
- 120Cevap
- E128
Cevap
120
By assigning a multiplier to the initial ratio , the counts are senior scientists, associate scientists, and junior researchers, making the initial total . Adding 8 senior scientists gives , and adding 4 promoted associate scientists gives . Equating their ratio to yields , which simplifies to , or . Multiplying by the total 10 parts gives the correct initial total of 120.
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Anahtar Kavram
Setting up and solving algebraic proportions involving multi-part ratios after internal transfers and external additions
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