What is the value of t?

Question

A hydroponic farm begins the week with t liters of nutrient solution in a holding tank. On Monday the farm used 1/4 of the solution in the tank. On Tuesday the farm used 1/3 of the solution that remained in the tank. The farm then added 90 liters of new solution, after which the tank held 6 liters more solution than it had held at the start of the week.

Accepted Answer

C. 168. After Monday, (3/4)t liters remain. Tuesday's use removes 1/3 of that remainder, leaving (2/3)(3/4)t = (1/2)t. Adding 90 gives (1/2)t + 90 = t + 6, so 84 = (1/2)t and t = 168. Check: 168 - 42 = 126; 126 - 42 = 84; 84 + 90 = 174 = 168 + 6. (A) 84 is the volume left after Tuesday's use: the student correctly reaches (1/2)t = 84 but reports 84 instead of solving for t. (B) 144 comes from taking Tuesday's 1/3 of the ORIGINAL amount rather than of the remainder, giving (5/12)t + 90 = t + 6. (D) 192 comes from reading '6 liters more' as 6 liters less, giving (1/2)t + 90 = t - 6.

Answer

A. 84 — 84 is the amount left in the tank after Tuesday's use — you correctly got (1/2)t = 84, but the question asks for t, so double it to 168.

Answer

B. 144 — You took Tuesday's 1/3 out of the original t instead of out of what remained after Monday; that gives (5/12)t + 90 = t + 6 and 144. Tuesday's fraction applies to the (3/4)t still in the tank.

Answer

D. 192 — You set up (1/2)t + 90 = t - 6, reading the ending amount as 6 liters *less* than the start. The tank ends with 6 liters more, so the right side is t + 6.

Algebra practice question

Answer: C. 168

Why the other answers are wrong

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