32. Two-part analysis
The two answers often share one constraint system. Solve jointly, answer separately.
Core ideas
- The two blanks usually share ONE constraint system. Set up the joint equations once, solve, then read off each answer separately.
- Do not solve each blank in isolation; the answer choices are designed so a blank-by-blank guess lands on a plausible wrong pair.
- The same value can appear as both answers, and the columns may use the same answer list. Check the instructions.
Worked example 1
A print shop sold 30 posters in a day. Small posters cost $2 each and large posters cost $5 each, and total revenue was $90. Select the number of small posters and the number of large posters sold.
Show solution
One system covers both blanks: s + l = 30 and 2s + 5l = 90. Substitute s = 30 - l: 2(30 - l) + 5l = 90, so 60 + 3l = 90 and l = 10, giving s = 20. Check: 2(20) + 5(10) = 40 + 50 = 90. Answer the blanks separately: small = 20, large = 10.
Worked example 2
Two pumps working together fill a 600-liter tank in 20 minutes. Pump A alone would take 30 minutes to fill the tank. Select Pump A's rate and Pump B's rate, each in liters per minute.
Show solution
The shared constraint is the combined rate: 600/20 = 30 liters per minute together. Pump A alone: 600/30 = 20 liters per minute. So Pump B's rate is the combined rate minus A's: 30 - 20 = 10 liters per minute. Check: at 30 L/min together, 20 minutes gives 600 liters. Answers: A = 20, B = 10.
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