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.
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<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.
Answer:
Step-by-step explanation:
d+q ≤ 16
She can have 16 or less than 16 coins (dimes and quarters) but no more than 16 coins
17 subtracted from x is:
x-17
x-17 is AT LEAST 19, meaning your inequality sign is going to be a greater than or equal to sign, since it says AT LEAST.
Your expression will be:
x-17≥19
Answer: a=225 adult, s=200 student
Explanation: We need a system of equations to find how many of each ticket Marc sold and we can use 4s+5a=1925 and s+a=425.
If we isolate a, we will have a=425-s
If we plug this into the first equation, we will get 4s+2125-5s=1925
Solving for s gives us s=200.
To find a, we can do 425-200 to find that a=225.
Answer:
8(h)=x
Step-by-step explanation:
Matt earns 8 dollars for every hour he works. So you multiply the total numbers worked (h) by 8. That will give you the amount of money he's made(x) so the equation would be 8(h)=x