Question

The Fundraiser Run Anna, Brad, Carly, Deonte, and Elijah ran around a track as part of a fundraiser for the school's math club. Anna ran first, and when she was tires, Brad ran. When Brad got tired, Carly ran, and so on. By the end of the fundraiser, they had run a total of 30 miles. Anna and Brad combined ran 12 miles. Brad and Carly combined ran 10.2 miles. Carly and Deonte combined ran 12 miles. Deonte and Elijah combined ran 12.3 miles. How far did each person run?

Answer 1

Input data

Anna ran first

Bran ran

Carly ran

Deonte ran

Elijah ran

They had run 30 miles

Anna + Brad 12 miles

Brad + Carly 10.2 miles

Carly + Deonte 12 miles

Deonte + Elijah 12.3 miles

Procedure

Let's solve a system of equations to find out how far the five athletes ran.

Let

A = Anna

B = Brad

C = Carly

D = Deonte

E = Elijah

`\begin{gathered} A+B+C+D+E=30 \\ A+B=12 \\ B+C=10.2 \\ C+D=12 \\ D+E=12.3 \end{gathered}`

Now we have a system of equations with 5 unknowns and 5 equations

Let us first calculate E

`\begin{gathered} (A+B)+(C+D)+E=30 \\ 12+12+E=30 \\ E=30-12-12 \\ E=30-24 \\ E=6 \end{gathered}`

Now let us calculate D

`\begin{gathered} D+E=12.3 \\ D=12.3-E \\ D=12.3-6 \\ D=6.3 \end{gathered}`

Now let us calculate C

`\begin{gathered} C+D=12 \\ C=12-D \\ C=12-6.3 \\ C=5.7 \end{gathered}`

Now let us calculate B

`\begin{gathered} B+C=10.2 \\ B=10.2-C \\ B=10.2-5.7 \\ B=4.5 \end{gathered}`

Finally, let us calculate A

`\begin{gathered} A+B=12 \\ A=12-B \\ A=12-4.5 \\ A=7.5 \end{gathered}`

Anwser

A = Anna ran 7.5 miles

B = Brad ran 4.5 miles

C = Carly ran 5.7 miles

D = Deonte ran 6.3 miles

E = Elijah ran 6 miles