To solve the problem, let's start by understanding the relationship between the number of cacti and flowering plants that Maria has. According to the problem, Maria has 7 more cacti than flowering plants. This can be written in the form of an equation:
[tex]\[ x = y + 7 \][/tex]
where [tex]\( x \)[/tex] is the number of cacti and [tex]\( y \)[/tex] is the number of flowering plants.
### Part (a): Complete the table
We will complete the table by filling in the values for [tex]\( x \)[/tex] (number of cacti) and [tex]\( y \)[/tex] (number of flowering plants) based on the given relationship [tex]\( x = y + 7 \)[/tex].
| Flowering plants (y) | Cacti (x) = y + 7 |
|----------------------|--------------------|
| 1 | 8 |
| 2 | 9 |
| 3 | 10 |
| 4 | 11 |
| 5 | 12 |
| 6 | 13 |
| 7 | 14 |
| 8 | 15 |
| 9 | 16 |
| 10 | 17 |
For example:
- If Maria has 1 flowering plant ([tex]\( y = 1 \)[/tex]), then she would have [tex]\( x = 1 + 7 = 8 \)[/tex] cacti.
- If Maria has 2 flowering plants ([tex]\( y = 2 \)[/tex]), then she would have [tex]\( x = 2 + 7 = 9 \)[/tex] cacti.
- This pattern continues for other values.
### Part (b): Write a number sentence linking [tex]\( x \)[/tex], [tex]\( y \)[/tex], and 7
The number sentence that links the number of cacti ([tex]\( x \)[/tex]) and the number of flowering plants ([tex]\( y \)[/tex]) with 7 is:
[tex]\[ x = y + 7 \][/tex]
This equation clearly states that the number of cacti is 7 more than the number of flowering plants.
