Bobby opened a bag of candy and counted how many pieces were in the bag. There were 68 pieces of orange, lime, and cherry candies in total. He separated them by flavor and found that there were 2 more orange than lime and 4 more cherry than orange. How many cherry candies were in the bag?

Number of limes are 20

Number of oranges are 22

Number of cherries are 26

Step-by-step explanation:

number of pieces of total candies = 68

Let the number of limes is y.

Number of orange = y + 2

Number of cherry = 4 + y + 2

So,

According to the question

y + y + 2 + 4 + 2 + y = 68

3 y + 8 = 68

3y = 60

y = 20

Number of limes are 20

Number of oranges are 22

Number of cherries are 26

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is