“The sum of 6 consecutive integers is 519” what is the third number in this sequence?

1 answer:

7 0

Let x be the first integer, then
:
x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) = 519
:
6x + 15 = 519
:
6x = 504
:
x = 84
:
*****************************
Our sequence is
:
84, 85, 86, 87, 88, 89
:
The third integer is 86

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The number of tickets they have sold in advance are summed up with the following equation and solution:

Equation: $\frac{6842.50}{17.50}$ [the final answer should be in dollars]

Solution: The Opera sold 391 tickets in advance.

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First: Review some background information:

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The Opera is collecting monies in advance for ticket sales. The tickets cost $17.50 each. If they have collected $6842.50 already, then how many tickets have they sold in advance?

We know how much the tickets cost and how much money they have earned from selling tickets, we can find out how much tickets they have sold.

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First we set up two fractions. One ticket costs $17.50, so we will use it to set up our first fraction: $\frac{1}{17.50}$ . We don't know how many tickets all together cost $6842.50 so we will use the variable: x. Now, we can set up our second fraction. x tickets costs $6842.50 so our second fraction will be: $\frac{x}{6842.50}$ . Now we must use cross multiplication. We multiply the numerator of the first fraction times the denominator of the second fraction, and then we multiply the denominator o the first fraction times the numerator of the second fraction. That's what we would do usually. But now, since we have a variable, we must use cross multiplication to solve for this variable. So we multiply the the numerator of the first fraction times the denominator of the other fraction and then we divide that answer times the denominator of the first fraction (You don't have to set it up like this).So let's solve this question: