Question

What fraction of the total money did T have at the beginning of the game?

• A. \(\frac13\)
• B. \(\frac15\)
• C. \(\frac29\)
• D. \(\frac15\)

Answer 1

The Correct Option is D

Step 1 — Translate the conditions into equations:
Let the money at the start be:
J = money with J,
B = money with B,
T = money with T.

From the problem:
(1) J + B = 4T
(2) T + B = 3J

Step 2 — Express all variables in terms of J:
From (2): T + B = 3J ⇒ T = 3J − B.
Substitute this into (1):
J + B = 4(3J − B).
J + B = 12J − 4B.
Bring terms together: J + B + 4B = 12J ⇒ J + 5B = 12J.
⇒ 5B = 11J − J = 11J − ? Wait, check carefully.
Actually: J + B = 12J − 4B ⇒ 5B = 11J.
So, B = (11/5)J.

Now substitute into T = 3J − B:
T = 3J − (11/5)J = (15/5 − 11/5)J = (4/5)J.

Step 3 — Find total money in terms of J:
Total = J + B + T.
= J + (11/5)J + (4/5)J.
= J + (15/5)J.
= J + 3J = 4J.

Step 4 — Fraction of total money that T had:
T = (4/5)J,
Total = 4J.
Fraction = T / Total = ((4/5)J) / (4J) = (4/5) ÷ 4 = 1/5.

Final Answer:
The correct option is (D): \(\tfrac{1}{5}\).