Square Roots
√4
2
A grocery store sells a 3-pound bag of apples for $4.50. What is the unit price of the apples per pound?
$1.50 per pound
X:3 = 12:18
2
A bakery sells a pack of 6 gourmet cupcakes for $15.90. What is the unit price per cupcake?
$2.65 per cupcake.
How many different types of cheese exist in the world?
Between 1,800 to 2,000 distinct types.
√400
20
Brand A sells 16 ounces of cereal for $3.68. Brand B sells 24 ounces of the same cereal for $5.28. Which brand offers a better deal per ounce?
Brand B is the better deal.
The relationship between oranges and apples is represented by the ratio 3:4. If I have 72 apples, how many oranges do I have?
54 Oranges
A supermarket offers two brands of apple juice. Brand A costs $4.20 for a 24-ounce bottle. Brand B costs $5.12 for a 32-ounce bottle. Which brand is the better buy, and what is its unit rate per ounce?
Brand B at $0.16 per ounce.
You are trapped between two doors; one leads to freedom and the other to danger. Two guards stand outside—one always tells the truth, and the other always lies. You can ask one guard a single question. What do you ask to guarantee your freedom?
Ask, "Which door would the other guard say leads to freedom?" Then, take the opposite door.
√181
13.4
An automated lawn sprinkler waters 3/4 of a lawn in 1/2 of an hour. What is the unit rate of the sprinkler in terms of the lawn fraction watered per hour?
3/2 or 1.5 lawns per hour.
A bag contains 3 different types of marbles: 2 Green, 8 Red, and 5 Blue. What is the ratio of Blue to Blue and Green marbles?
5:7
Julia is tracking her walking speed. She notices that she can walk 3/4 of a mile in every 1/6 of an hour. What is Julia's walking speed in miles per hour?
4.5 or 4 1/2 miles per hour.
Does a stellar object exist that does not emit light?
In reality, no. Theoretically, yes.
√15129
123
A submarine descends at a steady rate. It reaches a depth of 140 meters after 3.5 hours. How deep will it be after 6 hours?
-240 meters below the surface.
A math book comprises of two sections: math and more math in the ratio 8:6. How many pages of more math content will be needed to make a book of 980 pages?
420 Pages of More Math
An automated commercial painter can paint 2/5 of a standard wall in 1/3 of an hour. If the machine works at a constant speed, how many total hours will it take to paint 6 standard walls?
5 hours.
What is UpDog?
Nothing much, how about you?
√81+√21
13.5
A car travels 180 miles using 6 gallons of gas. Gasoline costs $3.25 per gallon. How much money will it cost to drive a total distance of 300 miles?
$32.50
The ratio of boys to girls in an art club is 4:5. If there are 45 total members in the club, and 6 more girls join the club, what is the new ratio of boys to girls?
20:31
A health shake recipe states that there are 150 calories in every 3/4 of a cup of the shake. Given that 1 cup = 8 fluid ounces, find the unit rate of calories per single fluid ounce
25 calories per fluid ounce.
A man looks at a photograph and says, "Brothers and sisters I have none, but that man's father is my father's son." Who is in the photograph?
His son. ("my father's son" must be the speaker himself, since he has no brothers or sisters. So the phrase becomes "that man's father is me.")