1.The entry tickets at a community fair cost $5 for children and $10 for adults. On a certain day 1000 people entered in the fair and \$7,100is collected. How many adults and how many children were at the fair? Please answer

The number of adult that were at fair are 480 adults

The number of children that were at fair are 580 children

Step-by-step explanation:

The given parameters are;

The entry tickets cost for children = $5

The entry ticket cost for adult = $10

The number of people that entered the fair on a certain day = 1,000

The amount collected for entry tickets sold = $7,100

Let 'x' represent the number of children that bought tickets and were at fair, and let 'y' represent the number of adults that bought tickets and were at the fair, we have;

x + y = 1,000...(1)

5·x + 10·y = 7,100...(2)

Making 'y' the subject of both equations gives;

For equation (1)

y = 1000 - x...(3)

For equation (2)

10·y = 7,100 - 5·x

y = (7,100 - 5·x)/10 = 710 - x/2

y = 710 - x/2...(4)

Equating both values of 'y' from equation (3) and equation (4), we have;

1000 - x = 710 - x/2

1000 - 710 = -x/2 + x = x/2

290 = x/2

x = 580

The number of children that bought tickets and were at fair = x = 580 children

From equation (3), y = 1,000 - x  = 1,000 - 580 = 420

y = 480

The number of adult that bought tickets and were at fair = y = 480 adults.

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