What is the solution for the proportion: 4 is to 25 as 70 is to x, and 20 is

Sure, let"s solve the proportion step by step.

We are given the proportion:

\(\frac{4}{25} = \frac{70}{x}\)

To find the value of \(x\), we can cross-multiply and then solve for \(x\).

Cross-multiplying means multiplying the numerator of the first fraction with the denominator of the second fraction, and vice versa.

Cross-multiplying the given proportion yields:

\(4 \times x = 25 \times 70\)

\(4x = 1750\)

Now, we can solve for \(x\) by dividing both sides of the equation by 4:

\(\frac{4x}{4} = \frac{1750}{4}\)

\(x = 437.5\)

Therefore, the solution for the proportion is \(x = 437.5\).

Now, let"s move on to the second part of the question.

The problem states that 20 is in proportion to this value of \(x\) we just found.

\(20\) is to \(437.5\) as ... is to \(437.5\).

To find the value that completes this proportion, we can again use cross-multiplication:

\(\frac{20}{437.5} = \frac{y}{437.5}\)

Cross-multiplying:

\(20 \times 437.5 = y \times 437.5\)

\(8750 = 437.5y\)

Now, divide both sides of the equation by 437.5 to solve for \(y\):

\(\frac{8750}{437.5} = \frac{437.5y}{437.5}\)

\(y = 20\)

Therefore, the solution for the second proportion is \(y = 20\).

In summary, the solution for the given proportion is \(x = 437.5\) and the second proportion is \(y = 20\).