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Practice set d

Garden A produces 5.8 times as many vegetables as garden B. Together the gardens produce 102 pounds of vegetables. How many pounds of vegetables does garden A produce?

  1. Let x =

Garden A produces 87 pounds of vegetables.

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Sample set e

Two consecutive even numbers sum to 432. What are the two numbers?

Step 1: Let x = the smaller even number . Then x + 2 = the next (consecutive) even number since consecutive even numbers differ by 2 (as do consecutive odd numbers) .
Step 2: x + x + 2 = 432. Step 3: x + x + 2 = 432 2 x + 2 = 432 2 x = 430 x = 215. Also, since x = 215 , x + 2 = 217.
Step 4 : 215 + 217 = 432 , but 215 and 217 are odd numbers and we are looking for even numbers . Upon checking our method of solution and reexamining our equation , we find no mistakes . Step 5 : We must conclude that this problem has no solution . There are no two consecutive e v e n numbers that sum to 432 .

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Practice set e

The sum of two consecutive even numbers is 498. What are the two numbers?

The two numbers are 248 and 250.

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Exercises

Solve the following problems. Note that some of the problems may seem to have no practical applications and may not seem very interesting. They, along with the other problems, will, however, help to develop your logic and problem-solving ability.

If eighteen is subtracted from some number the result is fifty-two. What is the number?

  1. Let x =
  2. The equation is
  3. (Solve the equation.)
  4. (Check)
  5. The number is .

Step 1: Let x = the unknown quantity.

Step 2: The equation is x 18 = 52.

Step 3: (Solve the equation.) Add 18 to each side.

     x 18 + 18 = 52 + 18

     x = 70

Step 4: (Check) 70 18 = 52 ; True.

Step 5: The number is 70.

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If nine more than twice a number is forty-six, what is the number?

  1. Let x =
  2. The equation is
  3. (Solve the equation.)
  4. (Check)
  5. The number is .

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If nine less than three eighths of a number is two and one fourth, what is the number?

  1. Let x =
  2. The number is .

Step 5: The number is 30.

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Twenty percent of a number is 68. What is the number?

  1. Let x =
  2. The number is .
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Eight more than a quantity is 37. What is the original quantity?

  1. Let x =
  2. The original quantity is .

Step 5: The original quantity is 29.

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If a quantity plus 85 % more of the quantity is 62.9 , what is the original quantity?

  1. Let x = original quantity.
  2. x original quantity + .85 x 85% more = 62.9
  3. The original quantity is .
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A company must increase production by 12 % over last year’s production. The new output will be 56 items. What was last year’s output?

  1. Let P =
  2. Last year’s output was items.

Step 5: Last year's output was 50 items.

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A company has determined that it must increase production of a certain line of goods by 1 1 2 times last year’s production. The new output will be 2885 items. What was last year’s output?

  1. Last year’s output was items.
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A proton is about 1837 times as heavy as an electron. If an electron weighs 2.68 units, how many units does a proton weigh?

  1. A proton weighs units.

Step 5: A proton weighs 4923 .16 units.

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Neptune is about 30 times as far from the sun as is the Earth. If it takes light 8 minutes to travel from the sun to the Earth, how many minutes does it take to travel to Neptune?

  1. Light takes minutes to reach Neptune.
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Questions & Answers

Wat d meaning of management
igwe Reply
disaster management cycle
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Fedric Wilson Taylor also define management as the act of knowing what to do and seeing that it is done in the best and cheapest way
OLANIYI
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Ugyen Reply
microeconomics is the study of individual units, firm and government while macroeconomics is the study of the economic aggregates.
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the situation that prevails when economic forces balance so that economic variables neither increase nor decrease
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salihu Reply
Economics is important because it helps people understand how a variety of factors work with and against each other to control how resources such as labor and capital get used, and how inflation, supply, demand, interest rates and other factors determine how much you pay for goods and services.
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the proces of using the services of labor and equipmnt together with other in puts to make goods and services availble
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Elacisity
salihu
Researchers demonstrated that the hippocampus functions in memory processing by creating lesions in the hippocampi of rats, which resulted in ________.
Mapo Reply
The formulation of new memories is sometimes called ________, and the process of bringing up old memories is called ________.
Mapo Reply
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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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