Respuesta :
To answer this item, we let x be the number of sessions at which the two rates would be equal.
For gym A, the total would become,
50 + 4x
while that of B is
30 + 6x
Equating these two expressions,
50 + 4x = 30 + 6x
The value of x from the equation is 10.
For gym A, the total would become,
50 + 4x
while that of B is
30 + 6x
Equating these two expressions,
50 + 4x = 30 + 6x
The value of x from the equation is 10.
The number of sessions for which the cost of the program will be same for each gym is 10
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, we can use three variables for number of sessions, and cost of program for each gym.
Let we have:
- n = Number of sessions
- a = Cost of program for n sessions for first gym
- b = Cost of program for n sessions for second gym
Then, by the given description, we get:
a = $(4 + 4 + ... + 4 (n times) ) + $50
or [tex]a = 4n + 50[/tex] (in dollars)
(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)
b = $( 6 + 6 + ... + 6 (n times) ) + $30
or [tex]b = 6n + 30[/tex] (in dollars)
The case when the cost of the program will be same for each gym, we will get:
a = b
or, from their corresponding expressions from aforesaid first two equations, we get:
[tex]4n + 50 = 6n + 30\\\\\text{Subtracting 4n + 50 from both the sides}\\4n + 50 - 4n - 50 = 6n + 30 - 4n - 50\\0n + 0 = 2n - 20\\0 = 2n - 20\\\text{Adding 20 on both the sides}\\20= 2n\\2n = 20\\\text{Dividing both the sides by 2}\\\dfrac{2n}{2} = \dfrac{20}{2} = 10\\n = 10[/tex]
Thus, the number of sessions for which the cost of the program will be same for each gym is 10
Learn more about system of linear equations here:
https://brainly.com/question/13722693
