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n200080 [17]
3 years ago
10

John divided his souvenir hat pins into two piles. The two piles had an equal number of pins. He gave his brother one-half of on

e-third of one pile. John had 66 pins left. How many pins did John originally have?
Mathematics
1 answer:
Serggg [28]3 years ago
5 0

Answer: John had 72 pins originally.

Step-by-step explanation:

Let x represent the total number of pins that John had originally.

John divided his souvenir hat pins into two piles. The two piles had an equal number of pins. This means that each pile has x/2 pins.

He gave his brother one-half of one-third of one pile. This means that the number of pins that he gave his brother is

1/2 × 1/3 × x/2 = x/12 pins

The total amount left is

x/2 + (x/2 - x/12) = x/2 + 5x/12 = 11x/12

John had 66 pins left. Therefore

11x/12 = 66

11x = 66 × 12 = 792

x = 792/11 = 72

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Substitute this equation x+3y=18 & -x-4y=-25
sveticcg [70]

Answer:

 {x,y} = {3/7,-43/7}

Step-by-step explanation:

System of Linear Equations entered :

  [1]    x + 3y = -18

  [2]    -x + 4y = -25

Graphic Representation of the Equations :

   3y + x = -18        4y - x = -25  

 

 

Solve by Substitution :

// Solve equation [1] for the variable  x  

 

 [1]    x = -3y - 18

// Plug this in for variable  x  in equation [2]

  [2]    -(-3y-18) + 4y = -25

  [2]    7y = -43

// Solve equation [2] for the variable  y  

  [2]    7y = - 43  

  [2]    y = - 43/7  

// By now we know this much :

   x = -3y-18

   y = -43/7

// Use the  y  value to solve for  x  

   x = -3(-43/7)-18 = 3/7  

Solution :

{x,y} = {3/7,-43/7}

5 0
3 years ago
Tim wants to build a rectangular fence around his yard. He has feet of fencing. If he wants the length to be twice the width, wh
Citrus2011 [14]

Answer:

how many feet of fencing does he have?

\

Step-by-step explanation:

8 0
3 years ago
Steve,Jerry and Ron were paid $29.25 to remove garden gnomes. They each worked 4 hours, exempt for Ron, who was 1 hour late. How
Alenkasestr [34]
Ron should receive $7.98. Jerry and Steve each worked for 4 hours, while Ron was one hour late, so he worked for 3 hours. Together, they worked for 4*2+3=11 hours, receiving $29.25 in total. Each hour should be paid 29.25/11=2.66 dollars. Ron worked for three hours, so he should receive 3*2.66=7.98 dollars. 
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Kyle is making a frame for a rectangular piece of art. The length of the frame is 3 times the width, as shown below.
NeX [460]

Answer:

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Step-by-step explanation:

The length of the frame is 3 times the width.

Let the width be x.

The length will be 3x.

Kyle uses 10 feet of wood to make the frame. This means that the perimeter is 10 feet.

The perimeter of a rectangle is:

P = 2(L + W)

=> 10 = 2(3x + x)

=> 10/2 = 4x

5 = 4x

=> x = 5/4 = 1.25 feet

The width is 1.25 feet. The length is therefore:

1.25 * 3 = 3.75 feet

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There are 25 servings in a 12.5 ounce bottle of olive oil. How many ounces are in a serving?
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If you divide 12.5 by 25 you should get 0.5

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