7)The admission fee at an agricultural fair is 2.50 for children and 6.00 for adults. On a certain day, 6200 people enter the fair and 29500 is collected. How many children and how manv adults attended? Write a linear system to model this situation

## Step 1: Define Variables<br />### Let 'c' represent the number of children and 'a' represent the number of adults.<br /><br />## Step 2: Set up the Equations<br />### Based on the problem, we can set up two equations:<br />### $c + a = 6200$ (Total number of people)<br />### $2.50c + 6.00a = 29500$ (Total money collected)<br /><br />## Step 3: Solve for One Variable<br />### Multiply the first equation by -2.5: $-2.5c - 2.5a = -15500$<br />### Add this modified equation to the second equation:<br />### $(-2.5c - 2.5a) + (2.5c + 6a) = -15500 + 29500$<br />### This simplifies to $3.5a = 14000$<br />### Divide both sides by 3.5: $a = \frac{14000}{3.5} = 4000$<br /><br />## Step 4: Solve for the Other Variable<br />### Substitute the value of 'a' (4000) back into the first equation:<br />### $c + 4000 = 6200$<br />### Subtract 4000 from both sides: $c = 6200 - 4000 = 2200$