Adult tickets to a play cost $1.75 each and student tickets cost $1.25 each. Suppose there are twice as many student tickets sold as adult tickets. If the income from the play was $850, how many of each type of ticket were sold?

200 adult tickets and 400 student tickets were sold.

Step-by-step explanation:

Let x represent the number of adult tickets that were sold.

Let y represent the number of student tickets that were sold.

Adult tickets to a play cost $1.75 each and student tickets cost $1.25 each. If the income from the play was $850, the expression would be

1.75x + 1.25y = 850- - - - - - - - - -1

Suppose there are twice as many student tickets sold as adult tickets. This is expressed as

y = 2x

Substituting y = 2x into equation 1, it becomes

1.75x + 1.25 × 2x = 850

1.75x + 2.5x = 850

4.25x = 850

x = 850/4.25

x = 200

y = 2x = 2 × 200

y = 400

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)