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Dafna1 [17]
3 years ago
8

Twice the sum of a number and 3 is equal to three times the difference of the number and 7. Find the number

Mathematics
1 answer:
Agata [3.3K]3 years ago
6 0

Answer:

The number is 27

Step-by-step explanation:

Let us change the word statement to an algebraic equation

→ Assume that the number is x

→ Twice the sum of a number and 3, means add x by 3, then multiply the sum by 2

→ The algebraic expression is 2(x + 3)

→ Three times the difference of the number and 7, means subtract x and 7, then multiply the difference by 3

→ The algebraic expression is 3(x - 7)

→ Equate the two expressions

∴ 2(x + 3) = 3(x - 7)

→ Simplify each side

∵ 2(x + 3) = 2(x) + 2(3) = 2x + 6

∵ 3(x - 7) = 3(x) - 3(7) = 3x - 21

∴ 2x + 6 = 3x - 21

Let us solve the equation to find x

→ Subtract 6 from both sides

∴ 2x + 6 - 6 = 3x -21 - 6

∴ 2x = 3x - 21

→ Subtract 3x from both sides

∴ 2x - 3x = 3x - 3x - 27

∴ -x = -27

→ Divide both sides by -1

∴ x = 27

The number is 27

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Step-by-step explanation:

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2 years ago
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List 5 fractions that are between 1/3 and 4/5
koban [17]

9514 1404 393

Answer:

  2/5, 7/15, 8/15, 3/5, 2/3

Step-by-step explanation:

If these fractions are expressed with a common denominator, that would be 3×5 = 15. Then the given fractions are 1/3 = 5/15, and 4/5 = 12/15. The numerators 5 and 12 differ by 7, so we can easily choose 5 fractions in that range:

  6/15 = 2/5

  7/15

  8/15

  9/15 = 3/5

  10/15 = 2/3

_____

<em>Alternate solutions</em>

There is no requirement for the fractions to be written any particular way or with any particular spacing. The limits in decimal are 1/3 = 0.3333...(repeating) and 4/5 = 0.8. We could choose the decimal fractions ...

  0.34, 0.40, 0.50, 0.60, 0.70

or

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7 0
3 years ago
How many more cents per item is 3 items for $10 than 2 items for $5? Express your answer to the nearest whole number.
fiasKO [112]
10/3: 3.33
5/2:2.50

3.33-2.50=0.83

Answer: 83 cents.

5 0
3 years ago
PLS QUICK I ONLY HAVE 2 HOURS
UNO [17]

Answer:

D

Step-by-step explanation:

As you can observe from the pattern, the numerator gets multiplied by 4 every increase in the sequence.

So , clearly, the 5th term will be = \frac{64*4}{5} =\frac{256}{5}

and the 6th term will be = \frac{256*4}{5} =\frac{1024}{5}

Therefore , D will be the answer.

6 0
2 years ago
What is the answer to this equation -14=d/15
expeople1 [14]

Answer:

d=-210

Step-by-step explanation:

multiply 15 to both sides

-14*15 =-210

the 15 on the side with d cancels

Now you have d=-210

Hope this helps!

3 0
3 years ago
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