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Setler [38]
3 years ago
7

5 times a number increased by 18 is the same as 36 more than times 4 times the number. Find the number

Mathematics
1 answer:
Tju [1.3M]3 years ago
3 0

Answer:

Step-by-step explanation:

Let's assume that that question is meant to read:

________________________________________________

" 5 times a number increased by 18 is the same as 36 more than 4 times the number.  Find the number ".

_______________________________________________

Let the variable "x" (i.e. the lower-case letter ex]—represent the unknown number—for which we are asked to solve.

If the question/problem is meant to read:

_________________________________

 "  5 times a number increased by 18 is the same as 36 more than 4 times the number.  Find the number ".

_________________________________

Then, treat the problem as:

_________________________________

  " 5 times [a number increased by 18] " ; {is the same as}:  " 36 more than [4 times the number]".  Find the number ".

_________________________________

Note that:  " {is the same as:}" ;  means:  "equals:} ;

So:  "...[a number; that is, an unknown number; that is, "x" ;  increased by "18" ]" ;  would be represented by:  "[x + 18]" .

5 times that value would be represented as:

  →  5* (x + 18) ;   or:   "  5(x + 18) " .

Then we add the:  " = " ["equals"] sign:

_________________________________

Then, we consider:  "... 36 more than [4 times the number]" .

    4 times the [unknown number]:  would be written as:

         →  " 4 * x " ;   or simply:  " 4x " .

→  "36 more than this [the above value; i.e. "4x" ;  would be represented by adding "36" to said value; as follows:

          →  " 4x + 36 " ;

_________________________________________

Now we can:

  1)  Write our expression as an equation;  and then:

  2)  Solve for the value for "x" ; our unknown number.

___________________________________________

 Here is the expression, as an equation:

________________________________________

  →  5(x + 18) =  4x + 36 ;

Now, solve for "x" ;

_________________________________________

Start with the "left-hand side" of the equation:

          →  5(x + 18) ;

Let us expand this expression.

___________________________________

Note the "distributive property" of multiplication:

   →  a(b+c) = ab + ac .

___________________________________

As such:  " 5(x + 18) = (5 * x)  +  (5 * 18) "  = 5x +120 .

Now, rewrite the equation:

  →  5x + 120 = 4x + 36 ;

Let us subtract "36" from each side of the equation; & subtract "4x" from each side of the equation:

                       →  5x + 120  =     4x  +  36 ;

                         - 4x   -  36  =   - 4x  -  36

                      ________________________

         to get:        1x +  54  =      10 ;

________________________________________

Rewrite as:      " x + 54 = 10 "  ;

→  {Since:  "1x = x " ;  

        → {since:  (" 1 * [any numerical value] = that same numerical value"};

        Note that this refers to the "identity property of multiplication."

___________________________________________

  →  

_________________________________________

 → We have:   " x + 54 = 10 " ;  Solve for "x" ;

Subtract "54" from Each Side of the equation;

 to isolate "x" on one side of the equation; & to solve for "x" ;

       →  " x + 54 - 54 = 10 - 54 " ;

 to get:  " x = -44 " .

_______________________________

Answer:  The number is " - 44 " .

_______________________________

Let us substitute this value into our equation;  to check our work:

→  5(x + 18) =  4x + 36 ;

→  5(-44 + 18) ≟ 4(-44) + 35 ??  ;

→  5(-26) ≟ -176 + 35 ?? ;

→  -130   ≟ -176 + 35

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6 0
3 years ago
There are 92,746 seats available for fans at UGA's Sanford Stadium. Auburn University's Jordan-Hare Stadium has seating for 87,4
Anvisha [2.4K]

Given :

Number of seats at UGA's Sanford Stadium, n_1 = 92,746 .

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How many more seats are there at UGA's stadium.

Solution :

Extra seats at UGA's stadium = seats at UGA's Sanford Stadium - seats at    

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= 92,746 - 87,451

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A random sample of size 100 was taken from a population. A 94% confidence interval to estimate the mean of the population was co
Firlakuza [10]

Answer:

Step-by-step explanation:

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The correct option is D

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The formula for normal distribution is expressed as

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7 0
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PLZ HELP ME!!!<br> 18 packages of basil cost $54. How many packages can you buy for $9?
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Answer:

3

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Possible
Alecsey [184]
<h3>Answer:  Independent</h3>

For two events A and B, if the occurrence of either event in no way affects the probability of the occurrence of the other event, then the two events are considered to be <u>  independent  </u> events.

=========================================================

Explanation:

Consider the idea of flipping a coin and rolling a dice. If these actions are separate (i.e. they don't bump into each other), then one object won't affect the other. Hence, one probability won't change the other. We consider these events to be independent.

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