This is question I need help with.
The annual gym subscription for a single member is $1000, while an annual family membership is $1500. The gym is considering increasing all membership fees by the same amount. If this is done then a single membership would cost of a family 5/7 membership. Write an equation to model the situation. Solve the equation to find the amount of the proposed increase. Write a sentence stating your
solution
If your garbled sentence means
"single membership would cost 5/7 of a family membership"
then you have
1000+x = 5/7 (1500+x)
x = 250
Thank you
To model the situation, we can start by considering the current cost of a single membership and the current cost of a family membership. Let's say the proposed increase is denoted by 'x'.
Currently, a single membership costs $1000, so if we increase it by 'x', the new cost would be $1000 + 'x'.
Similarly, a family membership costs $1500, and if we increase it by 'x', the new cost would be $1500 + 'x'.
According to the problem, the new cost of a single membership would be 5/7 of the new cost of a family membership. Mathematically, we can express this as:
1000 + 'x' = (5/7)(1500 + 'x')
To solve this equation and find the value of 'x', we can multiply through by 7 to eliminate the fraction:
7000 + 7('x') = 5(1500 + 'x')
Expanding the equation:
7000 + 7'x' = 7500 + 5'x'
Now, we can simplify and isolate the 'x' term on one side:
7'x' - 5'x' = 7500 - 7000
2'x' = 500
'x' = 500/2
'x' = 250
Therefore, the proposed increase in membership fees would be $250.
In summary, the solution is that the proposed increase in membership fees is $250.