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babunello [35]
3 years ago
6

Mark's school is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 4 senior tick

ets and 4 child tickets for a to total of 68. The school took in 120 on the second day by selling 12 senior tickets and 5 child tickets. Find the price of a senior ticket and a child ticket
Mathematics
1 answer:
erica [24]3 years ago
4 0

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

4 \times a + 4 \times b = 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:

12 \times a + 5 \times b = 120

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

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