Question

Three metallic tanks have the capacities of 447 litres, 577 litresand 669 litres. Find the capacity of the largest container that can fill the tanks an exact number of times, leaving a remainder of 7 litres, 5 litres and 9 litres respectively. (3 marks)​

Answer 1

To find the largest container that can fill each tank leaving specific remainders, we subtract the remainders from the capacities of the tanks and then find the GCD of the resulting numbers.

Step-by-step explanation:

The question deals with finding the capacity of the largest container that can fill three metallic tanks with specified capacities, such that when each tank is filled, a specific small remainder is left in each. To find the capacity of the container, we need to determine the greatest common divisor (GCD) of the amounts of liquid each tank can hold after the given remainders are subtracted.

The capacities of the tanks after subtracting the remainders are:

447 liters - 7 liters = 440 liters

577 liters - 5 liters = 572 liters

669 liters - 9 liters = 660 liters

To find the GCD of 440, 572, and 660 liters, we would typically use the Euclidean algorithm. After applying this algorithm, the largest container capacity would be the GCD of these three numbers.

Answer 2

44 litres

Step-by-step explanation:

We subtract the remainders from the amounts.

447 - 7 = 440

577 - 5 = 572

669 - 9 = 660

Now we need the GCF of 440, 572, 660

440 = 2³ × 5 × 11

572 = 2² × 11 × 13

660 = 2² × 3 × 5 × 11

GCF = 2² × 11 = 44

The greatest common factor is 44.

Answer: 44

Check:

447/44 = 10 reminder 7

577/44 = 13 remainder 5

669/44 = 15 remainder 9