Question

In what ratio must gold of 22 carats and 28 carats be mixed to get gold of 26 carats?​

Answer 1

Answer:

The two types of gold should be mixed in a ratio of 1:2 (or x:y = 1:2) to obtain gold of 26 carats.

Step-by-step explanation:

GIVEN DATA

22 and 28 carats of gold.

TO DETERMINE

The ratio in which the 22 carats and 28 carats are to be mixed to get 26 carats.

EVALUATION

Let us assume that x grams of 22-carat gold is mixed with y grams of 28-carat gold to obtain (x + y) grams of 26-carat gold.

To solve for x and y, we can use the concept of the average or weighted average of the carat values of the two types of gold.

The carat value of gold can be thought of as a concentration, and the concentration of the resulting gold can be expressed as the weighted average of the concentrations of the two types of gold:

$26 = \frac{(22x+28y)}{(x+y)}$

Simplifying the equation, we get:

26(x + y) = 22x + 28y

26x + 26y = 22x + 28y

4x = 2y

$\frac{x}{y} =\frac{1}{2}$

Therefore, the two types of gold should be mixed in a ratio of 1:2 (or x:y = 1:2) to obtain gold of 26 carats.

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Answer 2

The two types of gold should be mixed in a ratio of 1:2 to get the gold of 26 carats.

GIVEN:- 22 carats and 28 carats of gold

TO FIND:- In what ratio must gold of 22 carats and 28 carats be mixed to get gold of 26 carats

SOLUTION:-

• Let's assume that x grams of 22-carat gold are blended with y grams of 28-carat gold to procure (x + y) grams of 26-carat gold.
• For solving for x and y, we can use the theory of the average or weighted average of the carat values of the two kinds of gold.
• The carat value of gold can be thought of as a concentration, and the concentration of the occurring gold can be asserted as the weighted average of the concentrations of the two kinds of gold:

$26 = \frac{(22x + 28y)}{(x + y)}$

By simplifying the equation, we will get:

26(x + y) = 22x + 28y

26x + 26y = 22x + 28y

4x = 2y

Dividing both sides by 2

$\frac{4x}{2} = \frac{2y}{2} \\ 2x = y \\ \frac{x}{y} = \frac{1}{2}$

Hence, the two types of gold should be mixed in a ratio of 1:2 to get the gold of 26 carats.

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