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JJ joined a fresh food delivery service where he gets a box of fresh fruits and vegetables delivered at home. The service costs \[tex]$30 to join, and each box costs \$[/tex]10. Let [tex]\( E \)[/tex] represent the food expense related to this service and let [tex]\( B \)[/tex] represent the number of boxes he purchased.

i) Give an equation for [tex]\( E \)[/tex].

ii) Solve the equation you obtained in i) for [tex]\( B \)[/tex].

A.
i) [tex]\( E = 30 + 10B \)[/tex]
ii) [tex]\( B = \frac{E}{10} - 30 \)[/tex]

B.
i) [tex]\( E = 30 + 10B \)[/tex]
ii) [tex]\( B = \frac{E - 30}{10} \)[/tex]

C.
i) [tex]\( E = 10B \)[/tex]
ii) [tex]\( B = \frac{E}{10} \)[/tex]

D.
i) [tex]\( E = 10B \)[/tex]
ii) [tex]\( B = E - 10 \)[/tex]

Sagot :

GinnyAnsweridn
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]
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