Question

The bib numbers (# assigned to a runner upon registration) of four consecutive runners has a sum of1,830. Find the numbers of the four runners.

Answer 1

456, 457,458,459

Step-by-step 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

`\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} \\ (4x)/(4)=(1824)/(4) \\ x=456 \end{gathered}`

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