Respuesta :
456, 457,458,459
Explanation
Step 1
Let
x= the number of the runner (1)
then,
the number of runner (2) = x+1
the number of the runner (3) is = the number of the runner (2) +1
the number of the runner (3) is = x+1 +1=x+2
the number of the runner (3)=x+2
the number of the runner (4) is = the number of the runner (3) +1
the number of the runner (4) is = x+2 +1
the number of the runner (3) is =x+3
in other words, the 4 consecutive numbers are
x, x+1,x+2 and x+3
Step 2
the sum of the 4 consecutive numbers=1830
replace
x+(x+1)+(x+2)+(x+3)=1830
solve for x
[tex]\begin{gathered} x+\left(x+1\right)+\left(x+2\right)+\left(x+3\right)=1830 \\ x+x+1+x+2+x+3=1830 \\ \text{add similar terms} \\ 4x+6=1830 \\ \text{substract 6 in both sides} \\ 4x+6-6=1830-6 \\ 4x=1824 \\ \text{divide each side by 4} \\ \frac{4x}{4}=\frac{1824}{4} \\ x=456 \end{gathered}[/tex]Step 3
replace the value of x to find the numbers
x= the number of the runner (1) =456
number 1=456
the number of runner (2) = x+1=456+1
number 2 = 457
the number of runner (3) = x+2=456+2
number 3 = 458
the number of runner (4) = x+3=456+3
number 4 = 459
