The cooper family, consisting of 6 children and 2 adults, goes to the movies and pays a total of $86. the griffen birthday party, consisting of 10 children and 3 adults, pays a total of $139 for tickets. let x = the cost of a child ticket and y = the cost of an adult ticket. how much does a child's ticket cost and how much does an adult ticket cost?

The cost of child's ticket = $10

The cost of adult ticket = $ 13

Step-by-step explanation:

Let x be the cost of a child ticket and y be the cost of an adult ticket.

Then According to the question, we have

Multiply equation (1) by 3 and equation (2) by 2, then we have

Subtract equation (1) from equation (2), we have

Substitute the value of x in equation (1), we get

Hence, the cost of child's ticket = $10

The cost of adult ticket = $ 13

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: