Jasper is a florist, and he is putting together bouquets of tulips to sell in his store. Using the 300 tulips he has in stock, he wants to make a combination of small bouquets with 8 tulips each and large bouquets with 20 tulips each.
Which pairs (s,𝓁) represent possible numbers of small and large bouquets that Jasper could make?
a) (22,6)
b) (5,13)
c) (15,9)
d) (2/3, 14)
Let's first calculate the total number of tulips Jasper has:
300 tulips
Now, let's find out how many small bouquets he can make:
300 tulips / 8 tulips per small bouquet = 37.5 small bouquets
Since Jasper can't make half of a bouquet, he can make either 37 or 38 small bouquets.
Now, let's find out how many large bouquets he can make:
300 tulips / 20 tulips per large bouquet = 15 large bouquets
Now, let's check the pairs to see which ones are feasible:
a) (22,6)
Small bouquets: 22
Large bouquets: 6
Total tulips used: 22*8 + 6*20 = 176 + 120 = 296
This is feasible.
b) (5,13)
Small bouquets: 5
Large bouquets: 13
Total tulips used: 5*8 + 13*20 = 40 + 260 = 300
This is feasible.
c) (15,9)
Small bouquets: 15
Large bouquets: 9
Total tulips used: 15*8 + 9*20 = 120 + 180 = 300
This is feasible.
d) (2/3, 14)
Since Jasper can't make 2/3 of a bouquet, this pair is not feasible.
Therefore, the possible pairs are:
a) (22,6)
b) (5,13)
c) (15,9)