Respuesta :
The inequalities that can represent this situation if m is the number of songs Miguel can buy are:
- Option A: [tex]1 + 1.5m \leq25\\[/tex]
- Option E: [tex]25 \geq 1 + 1.5m[/tex]
How to form mathematical expression from the given description?
You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
For this case, it is provided that:
- The price of an account activation = $1.00
- The price of a song = $1.50
- Total amount that Miguel has = $25
- m = number of songs that Miguel can buy
If he buys m = 0, he doesn't need to open an account, thus, saving all money of gift.
Else, if he buys m > 0, then:
Let c = total cost he will have to pay for m songs.
m songs will cost [tex]1.50 \times m[/tex] dollars
Total cost he will have to pay = account activation charge + m songs; cost
[tex]c = 1 + 1.5m[/tex]
(we don't write symbols like of currency generally, and understand it from context. Also, sign of multiplication is often hidden if there are non numeric symbols and numbers being multiplied are written together)
Since we have limited money, so:
c needs to be less than or equal to $25
This is symbolically written as:
[tex]c \leq 25[/tex]
But since we've got [tex]c = 1 + 1.5m[/tex], thus:
[tex]1 + 1.5m \leq25\\[/tex] (option A).
This can be reversed as:
[tex]25 \geq 1 + 1.5m[/tex] (Option E)
(both things are same, as [tex]c \leq 25[/tex] or [tex]25 \geq c[/tex] both are same since if c is less than or equal to 25, then that means 25 is greater than or equal to c)
(the case when c= 0, we have 0 < 25, so it is also included in those two options, as a special case)
Thus, the inequalities that can represent this situation if m is the number of songs Miguel can buy are:
- Option A: [tex]1 + 1.5m \leq25\\[/tex]
- Option E: [tex]25 \geq 1 + 1.5m[/tex]
Learn more about inequalities here:
https://brainly.com/question/11901702
