A laboratory technician prepares a liquid mixture by combining compound X, compound Y, and… — SAT

A laboratory technician prepares a liquid mixture by combining compound $X$ , compound $Y$ , and water. The ratio of the volume of compound $X$ to the volume of compound $Y$ is $3$ to $5$ , and the ratio of the volume of compound $Y$ to the volume of water is $2$ to $3$ . If the technician prepares a total of $1,240$ milliliters of the mixture, how many milliliters of compound $Y$ are in the mixture?

A
240
400Cevap
C
496
D
600

Cevap

400

To determine the volume of compound

Y

in the mixture, we must find a common ratio that relates all three components. The ratio of compound

X

to compound

Y

3:5

, and the ratio of compound

Y

to water is

2:3

. The least common multiple of the parts for compound

Y

(

5

and

2

) is

10

. Multiplying the first ratio by

2

gives

X:Y = 6:10

. Multiplying the second ratio by

5

gives

Y:\text{water} = 10:15

. This yields the unified ratio

X:Y:\text{water} = 6:10:15

. The total number of parts is

6 + 10 + 15 = 31

. Since the total volume is

1,240

milliliters, each part is equivalent to

\frac{1,240}{31} = 40

milliliters. Since compound

Y

represents

10

parts of the ratio, its volume is

10 \times 40 = 400

milliliters.

Adım Adım Çözüm

Unify the two separate ratios into a single ratio for all three components.

The ratio of compound

X

to compound

Y

3:5

, and the ratio of compound

Y

to water is

2:3

. The least common multiple of the parts for compound

Y

(

5

and

2

) is

10

. Multiplying the terms of the first ratio by

2

yields

X:Y = 6:10

. Multiplying the terms of the second ratio by

5

yields

Y:\text{water} = 10:15

. This gives the combined ratio

X:Y:\text{water} = 6:10:15

This establishes a common baseline for all components, allowing direct comparison and calculation of their relative volumes.

Calculate the total parts of the ratio and determine the volume of a single part.

The total number of parts is

6 + 10 + 15 = 31

parts. Given the total volume of the mixture is

1,240

milliliters, the volume per part is

\frac{1,240}{31} = 40

milliliters.

This determines the scaling factor needed to calculate the actual volume of each ingredient in the total mixture.

Find the volume of compound

Y

by multiplying its ratio parts by the volume per part.

Compound

Y

has

10

parts in the unified ratio. The volume of compound

Y

10 \times 40 = 400

milliliters.

This calculates the final target volume requested by the question.

Anahtar Kavram

Solving multi-step ratio problems by finding a common term to unify multiple ratios.

Tahmini Süre:1m 30s

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru