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harina [27]
2 years ago
8

Find four consecutive integers such that if the sum of the first and third is increased by 10, the result is 6 greater than 4 ti

mes the fourth
Mathematics
1 answer:
kap26 [50]2 years ago
6 0
Four consecutive integers are four numbers in a row, with a difference of one between each of them.

x= first integer
x+1= second integer
x+2= third integer
x+3= fourth integer

sum= add
increased by 10= add 10
the result is= equal sign
6 greater than= add 6
4 times= multiply


EQUATION
(x + x + 2) + 10= (4(x + 3)) + 6
combine like terms on the left side

2x + 12= (4(x + 3)) + 6
multiply 4 by terms in parentheses

2x + 12= 4x + 12 + 6
combine like terms on right side

2x + 12= 4x + 18
subtract 4x from both sides

-2x + 12= 18
subtract 12 from both sides

-2x= 6
divide both sides by -2

x= -3 first integer


x+1= -2 second integer
x+2= -1 third integer
x+3= 0 fourth integer


ANSWER: The four consecutive integers are -3, -2, -1 and 0.

Hope this helps! :)
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3x - 3y + 2z = 7  
3x + 1y - 3z = -5  ⇒ 6x - 2y - 1z = 2 ⇒ 42x - 14y -   7z = 14
7x  - 1y - 2z = 0   ⇒ 7x - 1y - 2z = 0 ⇒ <u>42x -   6y - 12z = 0    </u>
                                                                      -20y - 19z = 14
                                                            -20y + 20y - 19z = 14 + 20y
                            <u />                                                   <u>-19z</u> = <u>14 + 20y</u>
                                                                                -19         -19
                                                                                    z = -14/19 - 1 1/19y
                                         3x - 3y + 2(-14/19 - 1 1/19y) = 7
                                              3x - 3y - 1 9/19 - 2 2/19y = 7
                                                     3x - 5 2/19y - 1 9/19 = 7
                                                     <u>      +1 9/19  +1 9/19        </u>
                                                                   3x - 5 2/19y = 8 9/19
                                                            3x - 3x - 5 2/19y = 8 9/19 - 3x
                             <u />                                            <u>-5 2/19y</u> = <u>8 9/19 - 3x</u> 
                                                                         -5 2/19        -5 2/19
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             3x - 3(-1 64/97 + 57/97x) + 2(-14/19 - 1 1/19y) = 7
                    3x + 4 95/97 + 1 74/97x - 1 9/19 - 2 2/19y = 7
                               4 74/97x - 2 2/19y + 3.5056972328 = 7
                               <u>                                -3.5056972328   -3.5056972328</u>
                                                          4 74/97x - 2 2/19y = 3.494302767
                                          4 74/97x + 2 2/19y - 2 2/19y = 3.494302767 + 22/19y
                                                                          <u>4 74/97x</u> = <u>3.494302767 + 2 2/19</u>
                                                                           4 74/97               4 74/97
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