A specialty paint manufacturing facility creates a custom dye by mixing three liquid conce… — GRE General Test

A specialty paint manufacturing facility creates a custom dye by mixing three liquid concentrates: Red, Yellow, and Blue. In the formulation, the ratio of the volume of Red concentrate to Yellow concentrate is $2 : 3$ , and the ratio of the volume of Yellow concentrate to Blue concentrate is $4 : 5$ . If a single storage vat contains $140\text{ liters}$ of this fully mixed custom dye, how many liters of Yellow concentrate are in the vat?

A
$32\text{ liters}$
$48\text{ liters}$ Cevap
C
$60\text{ liters}$
D
$70\text{ liters}$
E
$84\text{ liters}$

Cevap

48\text{ liters}

of Yellow concentrate

To find the volume of Yellow concentrate, first combine the given ratios (Red : Yellow = 2 : 3 and Yellow : Blue = 4 : 5) into a unified ratio by expressing Yellow with a common term. Multiplying the first ratio by 4 gives Red : Yellow = 8 : 12, and multiplying the second ratio by 3 gives Yellow : Blue = 12 : 15. The combined ratio Red : Yellow : Blue is 8 : 12 : 15, yielding a total of 8 + 12 + 15 = 35 parts. Yellow accounts for 12 out of 35 parts. Multiplying 12/35 by the total volume of 140 liters yields (12/35) * 140 = 48 liters.

Adım Adım Çözüm

Unify the two separate ratios into a single three-part ratio.

Red : Yellow =

2 : 3 = 8 : 12

and Yellow : Blue =

4 : 5 = 12 : 15

. Thus, Red : Yellow : Blue =

8 : 12 : 15

Yellow is the common component in both ratios. Finding a common multiple for Yellow's ratio term (LCM of 3 and 4 is 12) allows us to express all three quantities in a unified ratio scale.

Calculate the total number of ratio parts and determine Yellow's fraction of the total mixture.

Total parts =

8 + 12 + 15 = 35

. Yellow's fraction of the total volume =

\frac{12}{35}

To convert a part-to-part ratio into a part-to-whole ratio, divide the target component's ratio parts by the sum of all ratio parts.

Multiply Yellow's fraction by the total volume of the mixture.

Yellow volume =

\frac{12}{35} \times 140 = 12 \times 4 = 48\text{ liters}

Multiplying the part-to-whole fraction by the total volume yields the exact volume of Yellow concentrate present.

Anahtar Kavram

Combining pairwise ratios into a unified three-part ratio to determine part-to-whole proportions.

Tahmini Süre:1m 30s

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