Tickets to the concert were 2.50 for adults and 1.00 for students. 1,200 was collected and 750 tickets were sold.
1 answer:
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Answer:
1). System of equations- D + Q = 90 and D + 2.5Q = 175.50
2). There are 33 dimes and 57 quarters in the bank.
Step-by-step explanation:
Dylan has a bank that sorts coins as they are dropped in it.
A panel shows the total number of coins inside as well as the total value of these coins.
Let the number of dimes in the bank = D
and the number of quarters in the bank = Q
If the panel shows total number of coins = 90
Then the equation will be
D + Q = 90 -------(1)
And the panel displays the amount of the coins = $17.55
Then equation will be
0.10D + 0.25Q = 17.55 [1 Dime = $0.10 and 1 quarter = $0.25]
D + 2.5Q = 175.50 ------------(2)
Now we subtract equation (1) form equation (2)
D + 2.5Q - (D + Q) = 175.50 - 90
D + 2.5Q - D - Q = 85.5
1.5Q = 85.5
Q =
= 57
By putting Q = 57 in the equation (1)
D + 57 = 90
D = 90 - 57 = 33
Therefore, there are 33 dimes and 57 quarters in the bank.
We conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.
<h3>How to get the sum of the first 8 terms?</h3>
In an arithmetic sequence, the difference between any two consecutive terms is a constant.
Here we know that:
There are 7 times the common difference between these two values, so if d is the common difference:
Then the sum of the first 8 terms is given by:
So we conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.
If you want to learn more about arithmetic sequences:
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The answer is 12. This is the step by step
