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# I am thinking of two numbers in the ratio . The difference between the two numbers is . What is the sum of the two numbers?

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I am thinking of two numbers in the ratio . The difference between the two numbers is . What is the sum of the two numbers?

May 24, 2018

#3
+22884
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I am thinking of two numbers in the ratio 5 : 3 .

The difference between the two numbers is 90.

What is the sum of the two numbers?

$$\begin{array}{|lrcll|} \hline (1) & \frac{a}{b} &=& \frac{5}{3} \quad & | \quad \cdot b \\ & a &=& \frac53b \\\\ (2) & a-b &=& 90 \quad & | \quad a = \frac53b \\ & \frac53b - b &=& 90 \\ & \frac53b - \frac33 b &=& 90 \\ & \frac23b &=& 90 \quad & | \quad \cdot \frac32 \\ & b &=& 90 \cdot \frac32 \\ & b &=& 3\cdot 45 \\ & b &=& 135 \\ \\ & a &=& \frac53b \quad & | \quad b = 135 \\ & a &=& \frac53 \cdot 135 \\ & a &=& 5\cdot 45 \\ & a &=& 225 \\\\ & a+b &=& 225 + 135 \\ & \mathbf{a+b} & \mathbf{=} & \mathbf{360} \\ \hline \end{array}$$

The sum of the two numbers is 360

May 25, 2018

#1
+8469
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I am thinking of two numbers in the ratio . The difference between the two numbers is . What is the sum of the two numbers?

Hello guest!

$$\color{BrickRed}if\ (relationship\ R=\frac{a}{b}=a-b)\ then\\ relationship\ R=a-b\\ a=R+b\\ relationship\ R=\frac{a}{b}\\ b=\frac{a}{R}\\ a+b=R+b+\frac{a}{R}\\ \color{blue}a+b=\frac{R^2+a+bR}{R}$$

Did you mean something like that?

Greatings

!

May 24, 2018
edited by asinus  May 24, 2018
#2
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Sorry, the asy did not load

I am thinking of two numbers in the ratio 5 : 3 . The difference between the two numbers is 90. What is the sum of the two numbers?

May 25, 2018
#3
+22884
+1

I am thinking of two numbers in the ratio 5 : 3 .

The difference between the two numbers is 90.

What is the sum of the two numbers?

$$\begin{array}{|lrcll|} \hline (1) & \frac{a}{b} &=& \frac{5}{3} \quad & | \quad \cdot b \\ & a &=& \frac53b \\\\ (2) & a-b &=& 90 \quad & | \quad a = \frac53b \\ & \frac53b - b &=& 90 \\ & \frac53b - \frac33 b &=& 90 \\ & \frac23b &=& 90 \quad & | \quad \cdot \frac32 \\ & b &=& 90 \cdot \frac32 \\ & b &=& 3\cdot 45 \\ & b &=& 135 \\ \\ & a &=& \frac53b \quad & | \quad b = 135 \\ & a &=& \frac53 \cdot 135 \\ & a &=& 5\cdot 45 \\ & a &=& 225 \\\\ & a+b &=& 225 + 135 \\ & \mathbf{a+b} & \mathbf{=} & \mathbf{360} \\ \hline \end{array}$$

The sum of the two numbers is 360

heureka  May 25, 2018