Question

A group is going to a state fair. If childrens tickets are $7.50 per child and adult tickets are $12 per adult, how many of each can go to the fair for $200? Write a linear equality, graph it, and show several solutions on graph. !! Help

Answer 1

Let c = children tickets

Let c = children tickets Let a = adult tickets

Let c = children tickets Let a = adult tickets Let c to be in place of x

Let c = children tickets Let a = adult tickets Let c to be in place of xLet a to be in place of y

Answer:

7.50c+12a<or=200 (you would have a inequality since that is the maximum number you could pay and no other information is given)

the graph is above and the inequality in slop intercept format is y= -5/8x+ 16 2/3

Solutions for c: 0 <or= c <or= 26* *(since that is the maximum whole number you can have for $200)

Solutions for a: 0 <or= a <or= 16* *(since that is the maximum whole number you can have for $200)

Note: In order for find other solutions your cordatnate has to be a whole number (that is positive or zero) within the red area shaded. However there are many examples given for answer purposes.

Explanation:

$7.50 is the price of each children tickets and $12 is the price of each adult tickets and when combined equal to $200 so you can multiply the variables to get 7.5c+12a <or= 200.

To graph the inequality there's two ways;

Way 1: Change from standerd form to slope intercept form

1. Place 7.50c on the right side by subtracting 7.50c on each side of the inequality (the point is to islolate a); 7.50c - 7.50c + 12y < or = 200 - 7.50c. The 7.50c on the left side cancel each other out so we'll get 12a < or =200 - 7.50c
2. Isolate a by dividing both sides by 12; 12a/12= (200 - 7.50c)/12 that equals to a < or = -5/8c + 16 2/3
3. Find an appropriate scale and graph you can use the a-interpect and c-intercpt to make a line since this is less than or equal to you shade the region below the line

Way 2: Isolate your variables to get your x and y intercept

1. To find the a-interpect you make c equal to 0 so it would be 12a = 200
2. Divide 12 on both sides; 12a/12 =200/12. The a-interpect is 16 2/3
3. To find the c-intercpt you make a equal to 0 so it would be 7.50c = 200. Graph the point on your graph
4. Divide 7.50c on both sides; 7.50c/7.50 =200/7.50. The a-interpect is 26 2/3. Graph the point on your graph
5. Draw a continuous line from your two points