Juan is buying flowers for his mother. He has $18 to spend and sees that roses are $3 each and carnations are $1.50 each. He wants to buy 3 times as many carnations as roses and spend all of his money on flowers. Write a system of equations that models this situation. Is there a viable solution that meets Juan’s conditions? Explain.

Question

Juan is buying flowers for his mother. He has $18 to spend and sees that roses are $3 each and carnations are $1.50 each. He wants to buy 3 times as many carnations as roses and spend all of his money on flowers. Write a system of equations that models this situation. Is there a viable solution that meets Juan’s conditions? Explain.

Answer 1

Let r be the number of roses Juan buys and c be the number of carnations. We have the following information:

Roses cost $3 each, so the cost of the roses is: 3r
Carnations cost $1.50 each, so the cost of the carnations is: 1.5c
Juan wants to buy three times as many carnations as roses, so the equation that represents this relationship is: c = 3r
Juan has $18 to spend, so the total cost of the flowers must equal $18: 3r + 1.5c = 18

To solve this system of equations, we can substitute the value of c from the second equation into the third equation:

3r + 1.5(3r) = 18
3r + 4.5r = 18
7.5r = 18
r = 18 / 7.5
r = 2.4

Since we can't buy a fraction of a rose, there is no viable solution that meets Juan's conditions. Juan would need to adjust his budget or the number of flowers he wants to buy.