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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 7: Q20. (page 247)

Find the value of x.
$\frac{3 x + 5}{3} = \frac{18 x + 5}{7}$

Short Answer

Expert verified

The value of x is $\frac{20}{33}$ .

Step by step solution

01

Step 1. Given information.

The ratio here given is,

$\frac{3 x + 5}{3} = \frac{18 x + 5}{7}$

02

Step 2. Concept and Formula Used.

The properties of proportion,

if $\frac{a}{b} = \frac{c}{d}$ then, $a d = b c$

The given ratio is $\frac{3 x + 5}{3} = \frac{18 x + 5}{7}$ ,

03

Step 3. Use the property of proportion, if ab=cd then, ad=bc.

Then,

$\begin{array}{l} 7 (3 x + 5) = 3 (18 x + 5) \\ 21 x + 35 = 54 x + 15 (Usingdistributiveproperty) \\ 21 x 鈭� 54 x = 15 鈭� 35 \\ 鈭� 33 x = 鈭� 20 \end{array}$

04

Step 4. Divide both sides by -33.

$\begin{array}{l} \frac{鈭� 33 x}{鈭� 33} = \frac{鈭� 20}{鈭� 33} \\ x = \frac{20}{33} \end{array}$

Therefore, the value of x is $\frac{20}{33}$ .

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Most popular questions from this chapter

Refer to a triangle. Express the ratio of the height to the base in simplest form.

Express the ratio in simplest form.

$I T : D T$

Three numbers aren鈥檛 known, but the ratio of the numbers is $1 : 2 : 5$ . Is it possible that the numbers are $1, 2,$ and5. $10, 20,$ and $50 ?$ $3, 6,$ and $20 ?$ $x, 2 x,$ and $5 x ?$

For the figure shown, it is given that $\frac{K R}{R T} = \frac{K S}{S U}$ . Copy and complete the table.

Write the algebraic ratio in simplest form.

$\frac{3 a}{4 a b}$

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