Chapter 7: Q30. (page 247)

Given the proportions $\frac{x + y}{y} = \frac{r}{s}$ and $\frac{x - y}{x + y} = \frac{s}{y}$ , what can you conclude?

Short Answer

Expert verified

The solution of the proportion is, $r = x - y$

Step by step solution

Step 1. Given information.

$\frac{x + y}{y} = \frac{r}{s}$ and $\frac{x - y}{x + y} = \frac{s}{y}$

Given expression,

$\frac{x + y}{y} = \frac{r}{s}$ and $\frac{x - y}{x + y} = \frac{s}{y}$

Step 2. Solve the first equation.

$\Rightarrow \frac{x + y}{y} = \frac{r}{s}$

$\Rightarrow y r = s (x + y)$

$\Rightarrow y r = s x + s y \to (i)$

Step 3. Solve the second equation.

$\Rightarrow \frac{x - y}{x + y} = \frac{s}{y}$

$\Rightarrow s (x + y) = y (x - y)$

$\Rightarrow s x + s y = y x - y^{2}$

$\Rightarrow s x + s y = y x - y^{2} \to (ii)$

From equation (i) and (ii),

$\Rightarrow y r = y x - y^{2}$

Eliminating y from the whole equation,

$\Rightarrow r = x - y$

Therefore, the solution of the proportion is, $r = x - y$ .

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Given the proportions $\frac{x + y}{y} = \frac{r}{s}$ and $\frac{x - y}{x + y} = \frac{s}{y}$ , what can you conclude?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve the first equation.

Step 3. Solve the second equation.

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Given the proportions x+yy=rsand x-yx+y=sy, what can you conclude?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve the first equation.

Step 3. Solve the second equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Probability and Statistics

Pure Maths

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Given the proportions $\frac{x + y}{y} = \frac{r}{s}$ and $\frac{x - y}{x + y} = \frac{s}{y}$ , what can you conclude?