A shop had some red pens and blue pens. 60% of all the pens were red. After 40 red pens were sold and 20 blue pens were added, exactly 50% of the pens were red. How many pens were in the shop at first?
Show Worked Solution
Worked Solution
Step 1: Define a variable for the original total.
Let the original number of pens = T.
Original red pens = 60% × T = 0.6T
Original blue pens = 40% × T = 0.4T
Step 2: Write expressions after the changes.
Red pens after selling 40: 0.6T − 40
Blue pens after adding 20: 0.4T + 20
New total: T − 40 + 20 = T − 20
Step 3: Set up the equation using the new percentage.
Red pens are now 50% of the new total:
(0.6T − 40) = 0.5 × (T − 20)
0.6T − 40 = 0.5T − 10
Step 4: Solve for T.
0.6T − 0.5T = 40 − 10
0.1T = 30
T = 300
Step 5: Verify.
Original: 180 red, 120 blue. After: 140 red, 140 blue, total 280. 140 ÷ 280 = 50%. ✓
Answer: 300
Correct answer: 300
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