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Archy [21]
2 years ago
15

You lose an online auction for an autograph. Your losing bid of $28 is 40% of the winning bid. How much less was your bid than t

he winning bid?
Mathematics
1 answer:
TEA [102]2 years ago
5 0

Answer:

My bid was $42 less than the winning bid.

Step-by-step explanation:

The winning bid is x.

$28 is 40% of x

0.4x = 28

x = 28/0.4

x = 70

The winning bid was $70.

$70 - $28 = $42

Answer: My bid was $42 less than the winning bid.

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Solve the system of equations.
Xelga [282]

Answer:

  b.  x=1, y=2, z=3

Step-by-step explanation:

The system of equations ...

  • 3x +2y +z = 10
  • 9x -6y +z = 0
  • x -y -3z = -10

has solution (x, y, z) = (1, 2, 3) . . . . matches choice B.

_____

While it is convenient to solve this using a graphing calculator or web site, one can easily solve the system by hand.

Subtract the second equation from 3 times the first:

  3(3x +2y +z) -(9x -6y +z) = 3(10) -(0)

  12y + 2z = 30 . . . . simplify

Dividing this result by 2 gives ...

  6y +z = 15 . . . . . . [eq4]

Subtract 3 times the third equation from the first:

  (3x +2y +z) -3(x -y -3z) = (10) -3(-10)

  5y +10z = 40 . . . . simplify

  y + 2z = 8 . . . . . . . divide by 5 . . . . . [eq5]

The two equations [eq4] and [eq5] can be solved any of the ways you usually solve two equations in two variables. Here, we'll use the first equation to write an expression for z that we can substitute into the second equation.

  z = 15 -6y . . . . . subtract 6y from [eq4]

  y + 2(15 -6y) = 8 . . . . . substitute for z in [eq5]

  -11y +30 = 8 . . . . . simplify

  -11y = -22 . . . . . . . subtract 30

  y = 2 . . . . . . . . . . . divide by the coefficient of y

  z = 15 -6(2) = 3 . . . . substitute for y in our equation for z

Substituting these values for y and z into the third original equation gives ...

  x - 2 -3(3) = -10

  x -11 = -10 . . . . . . . . simplify

  x = 1 . . . . . . . . . . . . add 11

The solution to the above system of equations is (x, y, z) = (1, 2, 3).

_____

<em>Comment on the problem statement</em>

Math is generally unforgiving of imprecision. The given system of equations has no variable "z", and some other typos are apparently involved. That is why we rewrote the system to the equations shown above.

It is very easy to mistake z for 2, or g for 9, or o for 0, or 1 for 7. There are other confusions that are possible, as well. Letters I (eye) and l (ell) are easily confused, and may be confused with 1 (one) as well. Sometimes y and 4, or 4 and 9, can also be written so as to be difficult to tell apart. Great care must be taken when handwriting these symbols.

7 0
3 years ago
Instructions for a blanket call for 36 yards of yarn. A skein of yarn has 6 feet in in. How many skeins of yarn do you need?
Aloiza [94]
For this case the first thing you should know is the following unit conversion:
 1 yard = 3 feet
 Applying the conversion we have:
 6 * (1/3) = 2 yards
 Therefore the number of skeins of yarn is:
 N = (36) / (2)
 N = 18
 Answer:
 
You need 18 skeins of yarn
5 0
3 years ago
Two trucks leave a warehouse at the same time. One travels due east at an average speed of 50 miles per hour, and the other trav
Keith_Richards [23]

Answer:Since the vehicles are travelling in the exact opposite direction, the sum of their rates is the rate at which they are separating. 48 + 64 = 112 miles per hour of separation.

728 miles ÷ 112 miles/hour = 6.5 hours

Step-by-step explanation:

8 0
3 years ago
The width of a rectangular room is 80% of its length. If the length of the room is 20 meters, what is the area of the room? A= l
KIM [24]

Answer:320ft^2

Step-by-step explanation:

80% of 20 is 16, because 80% is 4/5 and 20 divided by 5 is 4, multiplied by 4 is 16. Area is L x W, so 16 times 20 is 320, and don't forget unit of measurement, ft^2 for area

7 0
3 years ago
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Suppose an automobile manufacturer designed a radically new lightweight engine and wants to recommend the grade of gasoline that
lapo4ka [179]

Answer:

this is very confusing to understand that you want.

Step-by-step explanation:

4 0
3 years ago
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