There are pencils in the box: 10 red ones, 8 blue, 8 green, 4 yellow. Let us take, with eyes closed, some number of pencils from the box. What is the least number of pencils we have to take in order to ensure that we get at least 4 pencils of the same color?

Step-by-step explanation:

GIVEN: There are pencils in the box: red ones, blue, green, yellow. Let us take, with eyes closed, some number of pencils from the box.

TO FIND: What is the least number of pencils we have to take in order to ensure that we get at least pencils of the same color.

SOLUTION:

Total number of red pencils

Total number of blue pencils

Total number of green pencils

Total number of yellow pencils

if we pick pencil, there can be pencil of each color

Least number of pencils we have to take in order to ensure that we get at least pencils of the same color is .

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer