Answer:
Two quantities are in direct proportion if an increase in one quantity leads to a proportional increase in the other quantity. In this case, the number of melons and the cost of melons are in direct proportion if an increase in the number of melons leads to a proportional increase in the cost of melons.
To check if the given statement is true, we can use the concept of unit rate. Unit rate is the rate for one unit of a given quantity. In this case, the unit rate for melons would be the cost of one melon.
If 7 melons cost £5, then the cost of one melon can be calculated by dividing the total cost by the number of melons:
Cost of one melon = Total cost / Number of melons
= £5 / 7
= £0.714 (rounded to 3 decimal places)
Now, let's calculate the cost of different numbers of melons and see if they are in direct proportion:
For 1 melon, the cost would be £0.714
For 2 melons, the cost would be £1.429
For 3 melons, the cost would be £2.143
For 4 melons, the cost would be £2.857
For 5 melons, the cost would be £3.571
For 6 melons, the cost would be £4.286
For 7 melons, the cost would be £5.000
As we can see, the cost of melons increases proportionally with the number of melons. Therefore, we can conclude that the number of melons and the cost of melons are in direct proportion