There are roses and lilies at a flower shop. Two roses cost $7 while three lilies cost $5. Billy bought some roses and lilies and paid $86. Which of the following can be the number of lilies he bought?1. 242. 213. 364. 155. None of the above

To solve this problem, we need to set up a system of equations based on the information given.

Let's denote the number of roses Billy bought as R and the number of lilies as L.

From the problem, we know that:

1. Two roses cost $7, so one rose costs$7/2 = $3.5. Therefore, the total cost of roses is 3.5R.
2. Three lilies cost $5, so one lily costs$5/3 = $1.67 (approximately). Therefore, the total cost of lilies is 1.67L.
3. The total cost of roses and lilies is $86.

So we can set up the equation: 3.5R + 1.67L = 86.

Now, we can substitute each of the given options for L into the equation and see which one works:

1. If L = 24, then 3.5R + 1.67*24 = 86, which simplifies to 3.5R + 40.08 = 86. This implies that R = (86 - 40.08) / 3.5 = 13.12, which is not a whole number, so this option is not possible.
2. If L = 21, then 3.5R + 1.67*21 = 86, which simplifies to 3.5R + 35.07 = 86. This implies that R = (86 - 35.07) / 3.5 = 14.55, which is not a whole number, so this option is not possible.
3. If L = 36, then 3.5R + 1.67*36 = 86, which simplifies to 3.5R + 60.12 = 86. This implies that R = (86 - 60.12) / 3.5 = 7.39, which is not a whole number, so this option is not possible.
4. If L = 15, then 3.5R + 1.67*15 = 86, which simplifies to 3.5R + 25.05 = 86. This implies that R = (86 - 25.05) / 3.5 = 17.41, which is not a whole number, so this option is not possible.

Therefore, the answer is 5. None of the above.