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Vesnalui [34]
3 years ago
8

Christian sold tickets to the game . Good seats were $5 each and poor seats cost $2 each. 210 people attended and paid $660. How

many of each type of seat were sold
Mathematics
1 answer:
Sholpan [36]3 years ago
5 0
People who purchased good seats will be labeled as a
people who purchased poor seats will be labeled as b
therefore...
5a + 2b = 660
a + b = 210
Now, all that has to be done is for the system to be solved.
-2(a+b=210)

5a + 2b = 660
-2a - 2a = -420

3a=240
a= 80
*3 people purchased good seats.

Now we can plug that number in

5(80) + 2b = 660
400 + 2b = 660
2b = 260
b = 130
*130 people purchased poor seats

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What are three consecutive integers whose product is 480 more than their sum?
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Answer:

The three numbers are 7 8 and 9

Step-by-step explanation:

Givens

  • Let the first number be n - 1
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  • Let the third number = n + 1

Equation

(n - 1)(n)(n + 1) - (n-1 + n + n+1) = 480

Solution

Multiply (n - 1) and (n + 1) = (n - 1)*(n + 1) = n^2 - 1

Multiply the second integer by the result of the first and third: n (n^2 - 1)

Add the three integers together: (x - 1) + (n - 1) + n = 3n  Combine these 2 steps

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Graph

The graph shows that the intercept point is n =8. This is the only way I can see to solve this cubic. There are no other real roots.

Answer

n - 1 = 7

n = 8

n + 1 = 9

Check

Product 7*8*9 = 504

Sum = 7 + 8 + 9 = 24

504 - 24 = 480 Which checks.

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