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.(4 points)

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.(4 points)

Answer 1

Let's call the number of roses "x" and the number of carnations "y".

The cost of the roses is $3 * x.
The cost of the carnations is $1.50 * y.
We know that the total amount of money Juan has to spend is $18, so:
3x + 1.50y = 18.
We also know that Juan wants to buy 3 times as many carnations as roses, so:
y = 3x.
We now have a system of equations:
3x + 1.50y = 18
y = 3x

To solve this system of equations, we need to substitute the value of y from the second equation into the first equation:
3x + 1.50(3x) = 18
3x + 4.5x = 18
7.5x = 18
x = 2.4

Since the value of x is not an integer, it is not possible for Juan to buy a non-fractional number of roses. Therefore, there is no viable solution that meets Juan's conditions.