A Factory named color splash is preparing for a large project and has produced…
2023
A Factory named color splash is preparing for a large project and has produced 474 liters of red paint, 426 liters of blue paint and 456 liters of green paint. The factory needs to create the minimum possible number of cans all of equals volume, for each paint color without mixing any of the paints. how many cans will be produced in total if the factory uses all the paints?
- A.
180
- B.
426
- C.
226
- D.
474
Attempted by 16 students.
Show answer & explanation
Correct answer: C
Key insight: To minimize the number of equal-volume cans without mixing colours, find the greatest common divisor (GCD) of the three volumes; that GCD is the largest possible volume per can.
Compute gcd(474, 426): 474 − 426 = 48, so gcd(474,426) = gcd(426,48). Then 426 = 48 × 8 + 42, so gcd(426,48) = gcd(48,42). Finally gcd(48,42) = 6.
Include the third amount: gcd(6, 456). Since 456 is divisible by 6, gcd(6,456) = 6.
So the largest equal can volume is 6 litres.
Number of cans for each colour: 474 ÷ 6 = 79; 426 ÷ 6 = 71; 456 ÷ 6 = 76.
Total cans = 79 + 71 + 76 = 226.
Answer: 226 cans in total.