1550.19 – Wrestlers on the Scale

When wrestling practice was over, Fallon jumped on the scale to see how her weight was doing. But Tara jumped on with her, so Fallon couldn’t tell how much she weighed. All Fallon and Tara could see was that their combined weight was 201 pounds. Then Tara pushed Fallon off the scale so she could see about her own weight, but Ryn jumped on. The combined weight of these two was 226 pounds.

Then Ryn pushed Tara off, but Fallon still wanted another try, so she jumped on with Ryn. Their combined weight was 219 pounds. Finally, the coach chased them away from the scale, but they remembered those three numbers and were able to figure out their individual weights, thus impressing their math teacher no end. Can you do it too?

Solution

If FF is Fallon's weight, TT is Tara's weight and RR is Ryn's weight, then

F+T=201F+R=226R+F=219\begin{aligned}F + T &= 201 \\F + R &= 226 \\R + F &= 219 \\\end{aligned}

F+T+T+R+R+F=6462(F+T+R)=646F+T+R=323F+2T+R=427\begin{aligned}F + T + T + R + R + F &= 646 \\2(F + T + R) &= 646 \\F + T + R &= 323 \\F + 2T + R &= 427 \\\end{aligned}

T=104,F=97,R=122T = 104, F = 97, R = 122