What is x in the following ration equation ⇒x:(2342+x)=825:1415?

Step 1 If a:b=c:d then a×d=b×c, hence x×1415=(2342+x)×825 or multiplying both sides by 258 14x15×258=2342+x or 7⧸14x3⧸15×5⧸254⧸8=2342+x 35x12=2342+x or 35x12−x=35x12−12x12=2342 or 23x12=2342 or x=⧸237⧸42×2⧸12⧸23 or x=27

Step 1 42x23+42x=8251415 Apply fraction cross multiply: if ab=cd then a×d=b×c 42x1415=(23+42x)825 Simplify 42x1415=1965x 1965x=(23+42x)825 multiply both sides by 5 1965x×5=(23+42x)825×5 Simplify 196x=85(23+42x) Expand 85(23+42x)=1845+3365x 196x=1845=3365x Subtract 3365x from both sides 196x−3365x=1845+3365x−3365x Simplify 6445x=1845 Myltiply both sides by 5 5×6445x=184×55 Simplify 644x=184 Divide both sides by 644 644x644=184644 Simplify x=27

Step 1 Cross-multiply x2342+x=8251415 x×(1415)=(825)×(2342+x) 1415x=825x+92525 Step 2 Subtract 825x from both sides 1415x−825x=825x+92525−825x 4675x=92525 Step 3 Multiply both sides by 7546 (7546)×(4675x)=(7546)×(92535) x=27

Step 1 If a:b=c:d then a×d=b×c, hence x×1415=(2342+x)×825 or multiplying both sides by 258 14x15×258=2342+x or 7⧸14x3⧸15×5⧸254⧸8=2342+x 35x12=2342+x or 35x12−x=35x12−12x12=2342 or 23x12=2342 or x=⧸237⧸42×2⧸12⧸23 or x=27

Step 1 42x23+42x=8251415 Apply fraction cross multiply: if ab=cd then a×d=b×c 42x1415=(23+42x)825 Simplify 42x1415=1965x 1965x=(23+42x)825 multiply both sides by 5 1965x×5=(23+42x)825×5 Simplify 196x=85(23+42x) Expand 85(23+42x)=1845+3365x 196x=1845=3365x Subtract 3365x from both sides 196x−3365x=1845+3365x−3365x Simplify 6445x=1845 Myltiply both sides by 5 5×6445x=184×55 Simplify 644x=184 Divide both sides by 644 644x644=184644 Simplify x=27

Step 1 Cross-multiply x2342+x=8251415 x×(1415)=(825)×(2342+x) 1415x=825x+92525 Step 2 Subtract 825x from both sides 1415x−825x=825x+92525−825x 4675x=92525 Step 3 Multiply both sides by 7546 (7546)×(4675x)=(7546)×(92535) x=27

Solved: "What is x in the following ration equation..."

High School
Algebra
Pre-Algebra
Ratios, rates, proportions

Seamus Kent

Answered question

2022-01-21

What is x in the following ration equation

\Rightarrow x : (\frac{23}{42} + x) = \frac{8}{25} : \frac{14}{15} ?

Answer & Explanation

Karlie Wilkins

Beginner2022-01-22Added 7 answers

Step 1
If $a : b = c : d$ then $a \times d = b \times c$ , hence
$x \times \frac{14}{15} = (\frac{23}{42} + x) \times \frac{8}{25}$
or multiplying both sides by $\frac{25}{8}$
$\frac{14 x}{15} \times \frac{25}{8} = \frac{23}{42} + x$
or
$\frac{7 ⧸ 14 x}{3 ⧸ 15} \times \frac{5 ⧸ 25}{4 ⧸ 8} = \frac{23}{42} + x$
$\frac{35 x}{12} = \frac{23}{42} + x$ or
$\frac{35 x}{12} - x = \frac{35 x}{12} - \frac{12 x}{12} = \frac{23}{42}$
or $\frac{23 x}{12} = \frac{23}{42}$
or $x = \frac{⧸ 23}{7 ⧸ 42} \times \frac{2 ⧸ 12}{⧸ 23}$
or $x = \frac{2}{7}$

Madelyn Townsend

Beginner2022-01-23Added 13 answers

Step 1
$\frac{42 x}{23 + 42 x} = \frac{\frac{8}{25}}{\frac{14}{15}}$
Apply fraction cross multiply: if $\frac{a}{b} = \frac{c}{d}$ then $a \times d = b \times c$
$42 x \frac{14}{15} = (23 + 42 x) \frac{8}{25}$
Simplify $42 x \frac{14}{15} = \frac{196}{5} x$
$\frac{196}{5} x = (23 + 42 x) \frac{8}{25}$
multiply both sides by 5
$\frac{196}{5} x \times 5 = (23 + 42 x) \frac{8}{25} \times 5$
Simplify
$196 x = \frac{8}{5} (23 + 42 x)$
Expand $\frac{8}{5} (23 + 42 x) = \frac{184}{5} + \frac{336}{5} x$
$196 x = \frac{184}{5} = \frac{336}{5} x$
Subtract $\frac{336}{5} x$ from both sides
$196 x - \frac{336}{5} x = \frac{184}{5} + \frac{336}{5} x - \frac{336}{5} x$
Simplify
$\frac{644}{5} x = \frac{184}{5}$
Myltiply both sides by 5
$5 \times \frac{644}{5} x = \frac{184 \times 5}{5}$
Simplify
$644 x = 184$
Divide both sides by 644
$\frac{644 x}{644} = \frac{184}{644}$
Simplify
$x = \frac{2}{7}$

RizerMix

Expert2022-01-27Added 656 answers

Step 1 Cross-multiply

\frac{x}{\frac{23}{42} + x} = \frac{\frac{8}{25}}{\frac{14}{15}}

x \times (\frac{14}{15}) = (\frac{8}{25}) \times (\frac{23}{42} + x)

\frac{14}{15} x = \frac{8}{25} x + \frac{92}{525}

Step 2 Subtract

\frac{8}{25} x

from both sides

\frac{14}{15} x - \frac{8}{25} x = \frac{8}{25} x + \frac{92}{525} - \frac{8}{25} x

\frac{46}{75} x = \frac{92}{525}

Step 3 Multiply both sides by

\frac{75}{46}

(\frac{75}{46}) \times (\frac{46}{75} x) = (\frac{75}{46}) \times (\frac{92}{535})

x = \frac{2}{7}

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Pre-Algebra

Didn't find what you were looking for?