An arithmetic series has seven terms. the first term is 5 and the last term is 53. find the sum of the series!
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The cost of each senior ticket is $ 5 and cost of each child ticket is $ 12
<em><u>Solution:</u></em>
Let "a" be the price of each senior ticket
Let "b" be the price of each child ticket
<em><u>On the first day of ticket sales the school sold 4 senior tickets and 4 child tickets for a to total of 68</u></em>
Thus a equation is framed as:
4 senior tickets x price of each senior ticket + 4 child tickets x price of each child ticket = 68
4a + 4b = 68 ---------- eqn 1
<em><u>The school took in 120 on the second day by selling 12 senior tickets and 5 child tickets</u></em>
Similarly, we frame a equation as:
12a + 5b = 120 ---------- eqn 2
<em><u>Let us solve eqn 1 and eqn 2</u></em>
<em><u>Multiply eqn 1 by 3</u></em>
12a + 12b = 204 -------- eqn 3
<em><u>Subtract eqn 2 from eqn 3</u></em>
12a + 12b = 204
12a + 5b = 120
( - ) --------------
7b = 84
b = 12
<em><u>Substitute b = 12 in eqn 1</u></em>
4a + 4(12) = 68
4a + 48 = 68
4a = 20
a = 5
Thus cost of each senior ticket is $ 5 and cost of each child ticket is $ 12