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The Answer

The Answer. The Question. The Phoenix Zoo charges $20 for adults and $10 for children. On a holiday weekend they sold 700 tickets (not including season passes or discounts). From those 700 tickets, they collected a total of $9000 .

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The Answer

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  1. The Answer

  2. The Question The Phoenix Zoo charges $20 for adults and $10 for children. On a holiday weekend they sold 700 tickets (not including season passes or discounts). From those 700 tickets, they collected a total of $9000. • Write a system of equations that can be used to find the number of child tickets, c, and the number of adult tickets, a, that were sold during the holiday weekend.

  3. Step 1: Define the variables a = the number of adult tickets sold c = the number of child tickets sold

  4. Step 2: Write one equation We know that the total number of tickets sold was 700. Therefore, the number of adult tickets sold plus the number of child tickets sold totaled 700. Thus, our first equation is: a + c = 700

  5. Step 3: Write a 2nd equation We know that the total amount of money collected was $9000. Each adult ticket cost $20, and each child ticket cost $10. So the number of adult tickets multiply by $20 plus the number of child tickets multiplied by $10 equals $9000. So our second equation is: 20a + 10c = 9000

  6. Step 4: Stack the equations a + c = 700 20a + 10c = 9000

  7. Step 5: Multiply a + c = 700 20a + 10c = 9000 We want to multiply one of the equations by some number so that when we add the equations together, one of the variables is eliminated. Let’s multiply the top equation by -10, so that -10c and 10c will add to 0 and be eliminated from our equation. That gives us: -10a – 10c = -7000 20a + 10c = 9000

  8. Step 6: Add the two equations -10a – 10c = -7000 20a + 10c = 9000 Now, when we add the two equations together, we get: 10a = 2000. Dividing both sides by 10 gives us: a = 200

  9. Step 7: Find the other variable Now that we know what a equals, we can find c by plugging in the value of a into one of our original equations. Let’s plug 200 into our first equation: a + c = 700 That gives us 200 + c = 700. We then solve for c by subtracting 200 from both sides, giving us: c = 500

  10. Solution So there were 200 adult tickets and 500 child tickets sold during the holiday weekend.

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