Answer:
x = 12
Step-by-step explanation:
Step 1: Define
f(x) = 4x + 6
f(x) = 54
Step 2: Substitute variables
54 = 4x + 6
Step 3: Solve for <em>x</em>
<u>Subtract 6 on both sides:</u> 48 = 4x
<u>Divide both sides by 4:</u> 12 = x
Step 4: Check
<em>Plug in x to verify it is a solution.</em>
f(12) = 4(12) + 6
f(12) = 48 + 6
f(12) = 54
Answer:
1.2%
Step-by-step explanation:
I did math
s = 2(lw + lh + wh)
Divide each side by 2 : s/2 = lw + lh + wh
Subtract 'lh' from each side: s/2 - lh = lw + wh
Combine the 'w' terms: s/2 - lh = w(l + h)
Divide each side by (l + h): (s/2 - lh) / (l + h) = w
Answer:
92 attendees had activity cards
Step-by-step explanation:
Let x be the number of students with activity cards. Then 130-x is the number without, and the total revenue is ...
7x +10(130 -x) = 1024
7x +1300 -10x = 1024 . . . . eliminate parentheses
-3x = -276 . . . . . . . . . . . . . collect terms; subtract 1300
x = 92 . . . . . . divide by 3
92 students with activity cards attended the dance.
_____
<em>Comment on the solution</em>
Often, you will see such a problem solved using two equations. For example, they might be ...
Let 'a' represent the number with an activity card; 'w' the number without. Then ...
- a+w = 130 . . . . the total number of students
- 7a +10w = 1024 . . . . the revenue from ticket sales
The problem statement asks for the value of 'a', so you want to eliminate w from these equations. You can do that using substitution. Using the first equation to write an expression for w, you have ...
w = 130-a
and making the substitution into the second equation gives ...
7a +10(130 -a) = 1024
This should look a lot like the equation we used above. There, we skipped the extra variable and went straight to the single equation we needed to solve.
