proportion

If (a - b)/b = 3/7, which of the following must also be true? A) a/b = -4/7 B) a/b = 10/7 C) (a + b)/b = 10/7 D) (a - 2b)/b = -11/7 We can rewrite (a - b)/b as: a/b - b/b = 3/7 Since b/b = 1, we have: a/b - 1 = 3/7 Since -1 = -7/7, we have: a/b - 7/7 = 3/7 Add 7/7 to each side: a/b - 7/7 +...

The denominator of a fraction is 4 more than the numerator. If 4 is added to the numerator and 7 is added to the denominator, the value of the fraction is 1/2. Find the original fraction. Let the original fraction be n/d. We're given: d = n + 4 (n + 4) / (d + 7) = 1/2 Cross multiply...

what integer is tripled when 9 is added to 3 fourths of it? Let the integer be n. Tripling an integer means multiplying it by 3. We're given: 3n = 3n/4 + 9 Since 3 = 12/4, we have: 12n/4 = 3n/4 + 9 Subtract 3n/4 from each side: 9n/4 = 9 Typing this equation into the search engine, we get: n = 4

If I have a reading average of 2 hours 30 minutes 0 seconds per 93.25 pages, how long would it take me to read 58 pgs? Set up a proportion, of reading time to pages where m is the number of minutes it takes you to read 58 pages. 2 hours and 30 minutes is: 60(2) + 30 120 + 30 150 minutes Our...

Suppose that 17 inches of wire costs 51 cents at the same rate, how many inches of wire can be bought for 42 cents? Set up a proportion of inches of wire to cost, were w equals the inches of wire at 42 cents. We have: 17/51 = w/42 Type this proportion into our search engine, we get: w = 14

If 1/2 cup of milk makes 8 donuts. How much cups it takes to make 28 donuts? Set up a proportion of cups to donuts, where c is the number of cups required to make 28 donuts: 1/2/8 = c/28 Cross multiply: 28(1/2) = 8c 8c = 14 Plugging this equation into our search engine, we get: c = 1.75

6 times the reciprocal of a number equals 2 times the reciprocal of 7. What is the number We've got two algebraic expressions here. Let's take it in parts: Term 1: The phrase a number means an arbitrary variable, let's call it x. The reciprocal is 1/x Multiply this by 6: 6/x Term 2...

If x/2y = 3/4, what is the value of y/x? Cross multiply this proportion: 4x = 3(2y) 4x = 6y Divide each side by x: 4x/x = 6y/x The x's cancel, and we have: 6y/x = 4 Divide each side by 6: 6y/6x = 4/6 The 6's on the left cancel, we have: y/x = 4/6 We can simplify this. Type in Simplify 4/6...

There are 40 grams in 5 prunes. How much gram of weight is in 34 prunes? Set up a proportion of grams to prunes where g is the number of grams in 34 prunes: 40/5 = g/34 Typing this proportion of 40/5 = g/34 into our search engine, we get: g = 272

If you can buy 1⁄3 of a box of chocolates for 6 dollars, how much can you purchase for 4 dollars? Write your answer as a fraction of a box. Set up a proportion of dollars to boxes where b is the number of boxes for $4: 6/1/3 = 4/b Cross multiply: 6b = 4/3 Multiply each side by 1/6 to isolate...

Mike cut 2 acres of grass in 30 minutes on his tractor. Which proportion would determine how many acres of grass Mike cut in 60 minutes? Let a be the number of acres of grass cut by Mike in 60 minutes. We have the following proportion: 2/30 = a/60 Typing this problem into our search engine, we...

Benny bought 8 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 47 cards left. How many cards did Benny start with? Let b be the number of baseball trading cards Benny started with. We have the following events: Benny buys...

Jeremy can plant 10 trees in 4 hours. How many trees can he plant in 10 hours? Set up a proportion of trees planted to hours where t is the number of trees planted in 10 hours. 10/4 = t/10 Type this expression into the search engine and we get t = 25. This means Jeremy can plant 25 trees in...

You receive 9 text messages in 12 minutes. What is the rate of text messages per hour? Set up a proportion of text messages to minutes. Remember, there are 60 minutes in an hour, so we have: 9/12 = t/60 where t is the number of text messages in 60 minutes (1 hour) Typing this into the search...

Our recipe calls for 2 eggs and 3 cups of sugar. if we want to use 5 eggs, how much sugar will we need? Set up a relational proportion for eggs to cups of sugar where s is the number of cups of sugar we need for 5 eggs. 2/3 = 5/s Plugging this into the search engine, we get 7.5 cups of sugar.

A camel can drink 15 gallons of water in 10 minutes. At this rate, how much water can the camel drink in 8 minutes? Set up a proportion of gallons of water to time where g is the number of gallons of water in 8 minutes. 15/10 = g/8 Run this problem through our proportion calculator to get g = 12.

Tarzan looked at 48 websites in 4 hours. At that rate, how many would he look at in 10 minutes? 48 websites per hour / 4 hours = 12 websites / hour Since an hour is 60 minutes, we have 12 / websites per 60 minutes = w / 10 minutes or 12/60 = w/10 Solving the proportion in our calculator...

In a basketball game, you make 8 of 20 free throws. If you continue this for the next 50 free throws, how many can you expect to make? We set up a proportion of made free throws to attempts. 8/20 = m/50 where m is the number of made free throws in 50 attempts. We type 8/20 = m/50 into the...

A baseball player gets 3 hits in the first 15 games of the season. If he continues hitting at the same rate, how many hits will he get in the first 45 games? We set up a proportion of hits to games where h is the number of hits the player gets in 45 games: 3/15 = h/45 Enter this into our...

A recipe calls for 2 tablespoons of olive oil for every 3 servings. How much olive oil will be needed for 6 servings? Set up a proportion of tablespoons to servings: 2/3 = o/6 where o is the number of tablespoons per 6 servings. Type 2/3 = o/6 into our search engine, and we get o = 4.