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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

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
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Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir 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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