Questions
\(\textbf{1)}\) 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?
The answer is \( 10\) males
\(\textbf{2)}\) In a store, the ratio of hats to shirts is \(4:5\). After \(4\) hats are taken away the new ratio is \(3:5\). How many shirts are in the store?
The answer is \( 20\) shirts
\(\textbf{3)}\)The length of a rectangle is 4 times the width. What is the ratio of the width to the perimeter?
The answer is \( 1:10 \)
\(\textbf{4)}\) A box contains only blue and red marbles. There are \(200\) marbles in the box. \(3/5\) of the marbles are blue. How many red marbles are there?
The answer is \( 80\) red marbles
\(\textbf{5)}\) 6 apples for $15, what is the unit rate?
The answer is \($2.50 \) per apple
\(\textbf{6)}\) John’s new sports car gets 165 miles on 11 gallons of gas. How many miles per gallon does the sports car get?
The answer is \(15\) mpg
\(\textbf{7)}\) 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?
The answer is \(3:2 \)
\(\textbf{8)}\) 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?
The answer is \(1,025 \) total students
\(\textbf{9)}\) In a classroom the ratio of boys to girls is 2:3. There are 25 students in the class. How many are girls?
\(b+g=50,\,\,\,3b=2g\)
15 girls (10 boys)
\(\textbf{10)}\) Anna volunteers at a pet shelter. They have cats and dogs. There are 36 pets in total at the shelter, and the ratio of dogs to cats is 4:5. How many cats are at the shelter?
\(c+d=40,\,\,\,5d=4c\)
20 cats (16 dogs)
\(\textbf{11)}\) The ratio of red marbles to green marbles is 2:7. There are 36 marbles in total. How many are red?
\(r+g=36,\,\,\,7r=2g\)
8 red marbles (28 green marbles)
\(\textbf{12)}\) 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.
\(\displaystyle \frac{\text{miles}}{\text{gallons}}\,\,\, \frac{345}{15}=\frac{x}{35}\)
\((15)\cdot(x)=(345)\cdot(35)\)
\(15x=12{,}075\)
\(x=805\)
Anna could drive 805 miles on 35 gallons of gasoline.
\(\textbf{13)}\) 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.
\(\displaystyle \frac{\text{problems}}{\text{hours}}\,\,\, \frac{24}{1.5}=\frac{x}{8}\)
\((1.5)\cdot(x)=(24)\cdot(8)\)
\(1.5x=192\)
\(x=128\)
Andy could create 128 homework problems in 8 hours.
\(\textbf{14)}\) 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?
\(\displaystyle \frac{\text{dollar}}{\text{square feet}}\,\,\, \frac{1000}{680}=\frac{1400}{x}\)
\((1000)\cdot(x)=(680)\cdot(1400)\)
\(1000x=952{,}000\)
\(x=952\)
$1400 rents a 952 square foot apartment.
\(\textbf{15)}\) 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?
\(\displaystyle \frac{\text{pages}}{\text{minutes}}\,\,\, \frac{3}{40}=\frac{18}{x}\)
\((3)\cdot(x)=(40)\cdot(18)\)
\(3x=720\)
\(x=240\)
It would take Mike 240 minutes to write an 18 page report.
\(\textbf{16)}\) 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?
\(\displaystyle \frac{\text{students}}{\text{parents}}\,\,\, \frac{4}{5}=\frac{x}{155}\)
\((5)\cdot(x)=(4)\cdot(155)\)
\(5x=620\)
\(x=124\)
There were 124 students at the softball game.
\(\textbf{17)}\) 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.
\(\displaystyle \frac{\text{interest}}{\text{total}}\,\,\, \frac{48}{1600}=\frac{x}{100}\)
\((1600)\cdot(x)=(48)\cdot(100)\)
\(1{,}600x=4{,}800\)
\(x=3\)
The loan has a 3% simple interest rate.
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