A merchant blends two types of coffee beans: Type A, which costs \12 per kilogram and cont… — GMAT

A merchant blends two types of coffee beans: Type A, which costs $\$12$ per kilogram and contains $15\%$ caffeine by weight, and Type B, which costs $\$18$ per kilogram and contains $25\%$ caffeine by weight. The merchant mixes Type A and Type B to create a $60$ -kilogram batch of Blend C. If the total cost of the $60$ -kilogram batch of Blend C is $\$936$ , what is the percentage of caffeine by weight in Blend C?

Cevap: 21 %

Cevap

The percentage of caffeine by weight in Blend C is 21%.

Solving the linear system for total mass (

A + B = 60

) and total cost (

12A + 18B = 936

) reveals that Blend C consists of 24 kg of Type A beans and 36 kg of Type B beans. Type A contributes

24 \times 0.15 = 3.6

kg of caffeine, and Type B contributes

36 \times 0.25 = 9.0

kg of caffeine. The total caffeine mass of 12.6 kg out of 60 kg total mass equals a concentration of

12.6 / 60 = 21\%

Adım Adım Çözüm

Formulate linear system for bean masses based on total weight and cost

A + B = 60

and

12A + 18B = 936

, solving to

A = 24

kg and

B = 36

The weight of each constituent bean type must be determined before total caffeine content can be evaluated.

Calculate caffeine mass from each component

Type A provides

3.6

kg (

24 \times 0.15

) and Type B provides

9.0

kg (

36 \times 0.25

)

Solute mass is found by multiplying total component weight by its percentage concentration.

Sum caffeine masses to find total caffeine in the mixture

Total caffeine =

3.6 + 9.0 = 12.6

The total amount of caffeine present in Blend C is the combined sum from both bean types.

Determine caffeine concentration percentage of Blend C

\frac{12.6}{60} \times 100 = 21\%

Concentration is calculated as the ratio of total solute mass to total solution mass expressed as a percentage.

Anahtar Kavram

Weighted concentration combined with multi-variable cost systems

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru