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Notes

Problems and Videos

Solve each proportion.

\(\textbf{1)}\) \( \displaystyle \frac{3}{25}=\frac{m}{75} \)

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The answer is \( m=9 \)

\(\textbf{2)}\) \( \displaystyle \frac{15}{c}=\frac{3}{2} \)

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The answer is \( c=10 \)

\(\textbf{3)}\) \( \displaystyle \frac{4}{3}=\frac{d-4}{12} \)

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The answer is \( d=20 \)

Show Work

\(\,\,\,\,\,\,\displaystyle \frac{4}{3}=\frac{d-4}{12} \)

\(\,\,\,\,\,\,3(d-4)=48\)

\(\,\,\,\,\,\,d-4=16\)

\(\,\,\,\,\,\,d=20\)

\(\,\,\,\,\,\,{/latex}The answer is [latex] d=20 \)

\(\textbf{4)}\) \( \displaystyle \frac{2}{5}=\frac{8}{3x-1} \)

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The answer is \( x=7 \)

\(\textbf{5)}\) \(\, \displaystyle \frac{48}{9}=\frac{m}{6} \)

Show Work and Answer

\( (9)\cdot(m)=(48)\cdot(6) \)

\(9m=288 \)

\(m=32\)

\(\textbf{6)}\) \(\, \displaystyle \frac{8}{25}=\frac{x}{30} \)

Show Work and Answer

\( (25)\cdot(x)=(8)\cdot(30) \)

\(25x=240 \)

\(x=\displaystyle \frac{240}{25} \)

\(x=\displaystyle \frac{48}{5}= \)\(9 \frac{3}{5}\)

\(\textbf{7)}\) \(\, \displaystyle \frac{1.8}{c}=\frac{3}{25} \)

Show Work and Answer

\( (3)\cdot(c)=(1.8)\cdot(25) \)

\(3c=45 \)

\(c=15\)

\(\textbf{8)}\) \(\, \displaystyle \frac{5}{21}=\frac{k}{49} \)

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\( (21)\cdot(k)=(5)\cdot(49) \)

\(21k=245 \)

\(k=11\frac{2}{3}\)

\(\textbf{9)}\) \( \displaystyle \frac{4}{10}=\frac{x}{1.25} \)

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The answer is \( x=.5 \)

\(\textbf{10)}\) \( \displaystyle \frac{3x-8}{2}=\frac{6x-5}{5} \)

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The answer is \( x=10 \)

\(\textbf{11)}\) Solve using giant ones. Show your work.
\(\, \displaystyle \frac{5}{6}=\frac{x}{8} \)

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\(\displaystyle \frac{4}{4} \cdot \frac{5}{6}=\frac{x}{8} \cdot \frac{3}{3} \)

\(\displaystyle \frac{20}{24}=\frac{3x}{24} \)

\(20=3x \)

\(\displaystyle \frac{20}{3}=x \)

\(\textbf{12)}\) Solve by isolating the variable. Show your work.
\(\, \displaystyle \frac{5}{6}=\frac{x}{8} \)

Show Work and Answer

\(\displaystyle 8 \cdot \frac{5}{6}=\frac{x}{8} \cdot 8 \)

\(\displaystyle \frac{40}{6}=x \)

\(\displaystyle \frac{20}{3}=x \)

\(\textbf{13)}\) Solve by busting the denominators. Show your work.
\(\, \displaystyle \frac{5}{6}=\frac{x}{8} \)

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\(\displaystyle 24 \cdot \frac{5}{6}=\frac{x}{8} \cdot 24 \)

\(\displaystyle \frac{120}{6}=\frac{24x}{8} \)

\(20=3x \)

\(\displaystyle \frac{20}{3}=x \)

\(\textbf{14)}\) Solve the proportion by cross multiplying. Show your work.
\(\, \displaystyle \frac{5}{6}=\frac{x}{8} \)

Show Work and Answer

\( (6)\cdot(x)=(5)\cdot(8) \)

\(6x=40 \)

\(x=\displaystyle \frac{40}{6} \)

\(x=\displaystyle \frac{20}{3} \)

\(\textbf{15)}\) At a school, exactly 410 students are seniors. 40% of the students at the school are seniors. How many students attend the school in total?

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The answer is 1,025 students

\(\textbf{16)}\) The ratio of males to females in a room is 2 to 5. If there are 35 people in the room, how many are male?

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The answer is \(10 \) people are male in the room

\(\textbf{17)}\) A box with 50 marbles has only blue and red marbles. If 20 marbles are red, what is the ratio of blue marbles to red marbles?

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The answer is \(3:2 \)

\(\textbf{18)}\) Anna drove her car 345 miles and used 15 gallons of gasoline. At the same rate, how many miles could she drive her car using 35 gallons of gasoline? Set up and solve a proportion.

Show Work and Answer

\(\displaystyle \frac{\text{miles}}{\text{gallons}}\,\,\, \frac{345}{15}=\frac{x}{35}\)

\((15)\cdot(x)=(345)\cdot(35)\)

\(15x=12{,}075\)

\(x=805\)

Anna could drive 805 miles on 35 gallons of gasoline.

\(\textbf{19)}\) Andy can create \(24\) homework problems in \(1 \frac{1}{2}\) hours. If he remains this efficient, how many homework problems can he create in 8 hours? Set up and solve a proportion.

Show Work and Answer

\(\displaystyle \frac{\text{problems}}{\text{hours}}\,\,\, \frac{24}{1.5}=\frac{x}{8}\)

\((1.5)\cdot(x)=(24)\cdot(8)\)

\(1.5x=192\)

\(x=128\)

Andy could create 128 homework problems in 8 hours.

\(\textbf{20)}\) An apartment with 680 square feet of floor space rents for $1000 a month. A larger apartment rents for $1400 a month. The cost per square foot for each office is the same. How much floor space is in the larger office?

Show Work and Answer

\(\displaystyle \frac{\text{dollar}}{\text{square feet}}\,\,\, \frac{1000}{680}=\frac{1400}{x}\)

\((1000)\cdot(x)=(680)\cdot(1400)\)

\(1000x=952{,}000\)

\(x=952\)

$1400 rents a 952 square foot apartment.

\(\textbf{21)}\) Mike can write 3 pages of a report in 40 minutes. At this speed, how many minutes will it take Mike to write a 18 page report?

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\(\displaystyle \frac{\text{pages}}{\text{minutes}}\,\,\, \frac{3}{40}=\frac{18}{x}\)

\((3)\cdot(x)=(40)\cdot(18)\)

\(3x=720\)

\(x=240\)

It would take Mike 240 minutes to write an 18 page report.

\(\textbf{22)}\) The ratio of students to parents at a softball game was 4 to 5. There were 155 parents at the game. How many students were at the game?

Show Work and Answer

\(\displaystyle \frac{\text{students}}{\text{parents}}\,\,\, \frac{4}{5}=\frac{x}{155}\)

\((5)\cdot(x)=(4)\cdot(155)\)

\(5x=620\)

\(x=124\)

There were 124 students at the softball game.

\(\textbf{23)}\) The bank will lend a business $1600 and charge $48 per month simple interest. What monthly interest rate will the students pay? Set up a proportion to solve.

Show Work and Answer

\(\displaystyle \frac{\text{interest}}{\text{total}}\,\,\, \frac{48}{1600}=\frac{x}{100}\)

\((1600)\cdot(x)=(48)\cdot(100)\)

\(1{,}600x=4{,}800\)

\(x=3\)

The loan has a 3% simple interest rate.

See Related Pages\(\)

\(\bullet\text{ Proportion Calculator }\)
\(\,\,\,\,\,\,\,\,\text{(Symbolab.com)}\)

\(\bullet\text{ Ratios and Proportions}\)
\(\,\,\,\,\,\,\,\displaystyle\frac{4}{3}=\frac{d-4}{12}…\)

\(\bullet\text{ Rational Expressions- Multiplying and Dividing}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{x^2+3x-4}{(x+4)(x+5)}\cdot \displaystyle\frac{x+5}{x-1}…\)

\(\bullet\text{ Rational Expressions- Adding and Subtracting}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{x-5}{x+3}+\frac{x+2}{x^2+5x+6}…\)

\(\bullet\text{ Direct, Inverse, and Joint Variation}\)
\(\,\,\,\,\,\,\,\,\) \(…\)

\(\bullet\text{ Complex Fractions}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{\frac{x}{5}+\frac{1}{3}}{\frac{1}{5}-\frac{1}{6}}…\)

\(\bullet\text{ Partial Fraction Decomposition}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{8x+10}{x^2+2x}=\displaystyle\frac{5}{x} + \frac{3}{x+2}…\)

In Summary

Proportions are equations that state that two ratios are equal. Ratios are like fractions and look at the quotient relationship between 2 numbers.

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