Let's address the problem step-by-step.
### i) Give an equation for [tex]\( E \)[/tex].
JJ joined a fresh food delivery service with the following costs:
- The service costs \[tex]$30 to join.
- Each box of fresh fruits and vegetables costs \$[/tex]10.
Let's denote:
- [tex]\( E \)[/tex] as the total food expense related to this service.
- [tex]\( B \)[/tex] as the number of boxes JJ purchased.
The total expense [tex]\( E \)[/tex] will be the sum of the initial joining cost and the cost of all the boxes purchased. Therefore, the equation for [tex]\( E \)[/tex] can be written as:
[tex]\[ E = 30 + 10B \][/tex]
### ii) Solve the equation you obtained in i) for [tex]\( B \)[/tex].
To solve for [tex]\( B \)[/tex] in the equation [tex]\( E = 30 + 10B \)[/tex], follow these steps:
1. Start with the equation:
[tex]\[ E = 30 + 10B \][/tex]
2. Isolate the term involving [tex]\( B \)[/tex]:
Subtract 30 from both sides to get:
[tex]\[ E - 30 = 10B \][/tex]
3. Solve for [tex]\( B \)[/tex]:
Divide both sides by 10:
[tex]\[ B = \frac{E - 30}{10} \][/tex]
So the equation solved for [tex]\( B \)[/tex] is:
[tex]\[ B = \frac{E - 30}{10} \][/tex]
### Summary:
i) The equation for [tex]\( E \)[/tex] is:
[tex]\[ E = 30 + 10B \][/tex]
ii) Solving this equation for [tex]\( B \)[/tex] gives:
[tex]\[ B = \frac{E - 30}{10} \][/tex]
Therefore, the correct answers are:
i) [tex]\( E = 30 + 10B \)[/tex]
ii) [tex]\( B = \frac{E - 30}{10} \)[/tex]
