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?
CLEAR CHECK
7g = 63
7(g – 3) = 42
7g – 3 = 42
g = 9
The equation that does NOT give the correct value of g is:
7(g – 3) = 42
The equation that does NOT give the correct value of g is:
7g = 63
To solve this problem, we need to figure out the number of guests, denoted by g, that Mika can bring to the gym if she pays $42.
At Mika's gym, she can bring 3 guests for free. After the first three, she must pay $7 per guest. So, the total cost of bringing g guests is:
Cost = $7 × (g - 3) + $0 × 3
Cost = $7(g - 3)
We are given that the cost is $42, so setting up the equation:
$7(g - 3) = $42
Now we can solve for g.
7(g - 3) = 42
Divide both sides by 7 to isolate (g - 3):
(g - 3) = 6
Add 3 to both sides to solve for g:
g = 9
So, g = 9 is the correct value of the number of guests Mika can bring to the gym if she pays $42.
Now, let's analyze the given equations:
1. 7g = 63 - This equation states that the cost of bringing g guests is $63. This equation does not match the given scenario because Mika is paying $42, not $63. Therefore, this equation does NOT give the correct value of g.
2. 7(g - 3) = 42 - This equation is the correct equation we derived earlier. It states that the cost of bringing g guests, after subtracting the initial 3 free guests, is $42. Therefore, this equation gives the correct value of g.
3. 7g - 3 = 42 - This equation states that the cost of bringing g guests minus 3 is $42. However, the equation is incorrect because the 3 should be multiplied by 7 instead of subtracted from 7g. Therefore, this equation does NOT give the correct value of g.
Therefore, the equation that does NOT give the correct value of g is 7g = 63.