Explanation:
To find how many of the same cards the farmer can form at most, we need to find the greatest common factor (GCF) of 78 and 90. One way to do this is to list the factors of each number and find the largest one they have in common:
78: 1, 2, 3, 6, 13, 26, 39, 78
90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The largest factor they have in common is 6, so the farmer can form at most 6 baskets of the same size.
To find how much the farmer gets from the sale of 10 baskets, we need to first find the total number of artichokes and courgettes he has:
78 + 90 = 168
Next, we can find the total amount of money he gets from selling the artichokes and courgettes:
Money from artichokes = 78 × $0.70 = $54.60
Money from courgettes = 90 × $0.40 = $36.00
Total money = $54.60 + $36.00 = $90.60
If the farmer sells 10 baskets, then each basket would have 168/10 = 16.8 artichokes and courgettes. Since he can only form baskets of the same size, he would sell 6 baskets with 16 artichokes and 24 courgettes in each basket. The total amount of money he would get from selling these 6 baskets is:
Money from artichokes = 6 × 16 × $0.70 = $67.20
Money from courgettes = 6 × 24 × $0.40 = $57.60
Total money = $67.20 + $57.60 = $124.80
Therefore, the farmer would get $124.80 from the sale of 10 baskets.