Final answer:
The price of one Tulip (T) is 1,500 L.L., and the price of one Rose (R) is 2,500 L.L. To form a bunch of 6 flowers costing 10,000 L.L., we could choose 2 Tulips and 4 Roses.
Step-by-step explanation:
The question involves finding the price of a single Tulip and a single Rose using a system of linear equations, and then forming a bunch of flowers with a specific cost. Let's denote the price of a Tulip as 'T' and the price of a Rose as 'R'.
We are given two equations based on the bunches of flowers:
- 2T + 4R = 13,000 L.L. (For the bunch of 2 Tulips and 4 Roses)
- T + 5R = 14,000 L.L. (For the bunch of 1 Tulip and 5 Roses)
By solving these equations, we can find the individual prices of Tulips and Roses.
First, multiply the second equation by 2 to help eliminate 'T':
Now, subtract the first equation from this result:
- (2T + 10R) - (2T + 4R) = (28,000 L.L.) - (13,000 L.L.)
- 6R = 15,000 L.L.
- R = 2,500 L.L. (Price of one Rose)
Substitute 'R' back into one of the original equations to find 'T':
- 2T + 4(2,500 L.L.) = 13,000 L.L.
- 2T + 10,000 L.L. = 13,000 L.L.
- 2T = 3,000 L.L.
- T = 1,500 L.L. (Price of one Tulip)
To form a bunch of 6 flowers costing 10,000 L.L., we have the equation:
- xT + yR = 10,000 L.L. where x + y = 6
Choosing different combinations of Tulips and Roses whose total cost adds up to 10,000 L.L. while the total number of flowers remains 6, we can find an affordable bunch. For instance, 2 Tulips and 4 Roses, which would cost 3,000 L.L. + 2,500 L.L. x 4 = 10,000 L.L.