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.
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.
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