Mika’s gym allows her to bring 3 guests for free. After the first three, she must pay $7 per guest. How many guests, g, can she bring to the gym if she pays $42?
Three of these equations give the correct value of g. Which equation does NOT?
Let's define the equation that represents the scenario:
Total cost = $7 per guest × number of additional guests
If Mika pays $42, it means she has exceeded the 3 free guests, so she must have brought additional guests.
To find the number of additional guests (g), we divide the total cost by $7 per guest and subtract 3 (since the first 3 guests are free):
g = (Total cost / $7 per guest) - 3
Plugging in the given values:
g = ($42 / $7 per guest) - 3
g = 6 - 3
g = 3
So, Mika can bring 3 additional guests to the gym if she pays $42.
To check which equation does NOT give the correct value of g, let's substitute the values from each equation:
1) g = ($42 / 7) - 3
g = 6 - 3
g = 3
2) g = ($42 - 7) / 3
g = 35 / 3
g ≈ 11.67 ≈ 12
3) g = 42 / 7 - 3
g = 6 - 3
g = 3
So, equation 2) does NOT give the correct value of g.
Let's solve this step-by-step.
We know that Mika can bring 3 guests for free. After that, she must pay $7 per guest.
Let's assume Mika can bring "g" guests to the gym.
For the first 3 guests, she doesn't have to pay anything, so that's $0.
For the remaining guests, after the first three, she must pay $7 per guest.
So, the total amount she needs to pay for the remaining guests would be (g - 3) * $7.
To find the total amount paid by Mika, we add the cost for the first 3 guests and the cost for the remaining guests:
Total amount paid = $0 (for the first 3 guests) + (g - 3) * $7.
According to the problem, Mika pays $42, so we can set up the equation:
$0 + (g - 3) * $7 = $42.
Now let's solve the equation:
(g - 3) * $7 = $42.
Dividing both sides by $7, we have:
g - 3 = 6.
Adding 3 to both sides, we get:
g = 9.
So, according to the equation, Mika can bring 9 guests to the gym if she pays $42.
To determine which equation does NOT give the correct value of g, we need to compare the value of g obtained (g = 9) with each equation provided. Since we don't have the equations provided, I cannot determine which equation does NOT give the correct value of g. Please provide the equations for further assistance.
To find the number of guests, g, Mika can bring to the gym, we need to set up an equation based on the given information.
First, we know that Mika can bring 3 guests for free. So, the number of guests up to this limit is already covered without any cost.
After the first three guests, she has to pay $7 per guest. So, for each additional guest, she will have to pay $7.
Let's assume the number of guests beyond the initial 3 is x. So, the total number of guests will be 3 (initial guests) + x (additional guests).
We also know that Mika pays $42 in total for all the guests she brings. Therefore, we can set up the equation:
3 + x guests * $7 per guest = $42
Now let's solve the equation to find the value of x (additional guests) and then calculate the total number of guests, g.
3 + 7x = 42
7x = 39
x = 39/7
x ≈ 5.57
Since we cannot have a fractional number of guests, we need to round down the value of x to a whole number because Mika cannot bring a fraction of a guest.
So, the number of additional guests, x, is approximately 5.
Now, let's calculate the total number of guests, g:
g = 3 (initial guests) + x (additional guests)
g = 3 + 5
g = 8
Therefore, Mika can bring a total of 8 guests to the gym if she pays $42.
Now, let's analyze the given equations to identify the one that does not give the correct value of g.
1. g = 3 + 5 (from our calculation) which is equal to 8, so it is correct.
2. g = 3 + 7 - 42/7 = 8 - 6 = 2, which is incorrect.
3. g = 3 + 7 - 6 = 4, which is incorrect.
Therefore, the equation that does NOT give the correct value of g is g = 3 + 7 - 42/7.