# CONSTANT OF PROPORTIONALITY WORKSHEET

Problem 1 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality. Problem 2 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality. Problem 3 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality. Problem 4 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality. Problem 5 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality. Problem 6 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality. Problem 7 :

y is directly proportional to x. Given that y = 144 and x = 12. Find the value of y when  x = 7.

Problem 8 :

7 men can complete a work in 52 days. In how many days will 13 men finish the same work? ## Solutions

Problem 1 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality. Solution :

Let us get the ratio of x and y for all the given values.

4 / 48  =  1 / 12

7 / 84  =  1 / 12

10 / 120  =  1 / 12

When we take ratio of x and y for all the given values, we get equal value for all the ratios.

Therefore the relationship given in the table is proportional.

When we look at the above table when x gets increased, y also gets increased, so it is direct proportion.

Then, we have

y  =  kx

Substitute 4 for x and 48 for y.

48  =  k(4)

12  =  k

So, the constant of proportionality is 12.

Problem 2 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality. Solution :

Let us get the ratio of x and y for all the given values.

1 / 100  =  1 / 100

3 / 300  =  1 / 100

5 / 550  =  1 / 110

6 / 600  =  1 / 100

When we take ratio of x and y for all the given values, we don't get equal value for all the ratios.

So, the relationship given in the table is not proportional.

Problem 3 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality. Solution :

Find the ratio of x and y for all the given values.

2 / 1  =  2

4 / 2  =  2

8 / 4  =  2

10 / 5  =  2

When we take ratio of x and y for all the given values, we get equal value for all the ratios.

Therefore, the relationship given in the table is proportional.

When we look at the above table when x gets increased, y also gets increased, so it is direct proportion.

Then, we have

y  =  kx

Substitute 2 for x and 1 for y.

1  =  k(2)

1 / 2  =  k

So, the constant of proportionality is 1/2.

Problem 4 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality. Solution :

Find the ratio of x and y for all the given values.

1 / 2  =  1 / 2

2 / 4  =  1 / 2

3 / 6  =  1 / 2

4 / 6  =  2 / 3

When we take ratio of x and y for all the given values, we don't get equal value for all the ratios.

So, the relationship given in the table is not proportional.

Problem 5 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality. Solution :

Find the ratio of x and y for all the given values.

1 / 23  =  1 / 23

2 / 36  =  1 / 18

5 / 75  =  1 / 15

When we take ratio of x and y for all the given values, we don't get equal value for all the ratios.

So, the relationship given in the table is not proportional.

Problem 6 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality. Solution :

Find the ratio of x and y for all the given values.

2 / 4  =  1 / 2

4 / 8  =  1 / 2

6 / 12  =  1 / 2

8 / 16  =  1 / 2

When we take ratio of x and y for all the given values, we get equal value for all the ratios.

Therefore the relationship given in the table is proportional.

When we look at the above table when x gets increased, y also gets increased, so it is direct proportion.

Then, we have

y  =  kx

Substitute 2 for x and 4 for y.

4  =  k(2)

2  =  k

So, the constant of proportionality is 2.

Problem 7 :

y is directly proportional to x. Given that y = 144 and x = 12. Find the value of y when  x = 7.

Solution :

Because y directly proportional to x, we have

y  =  kx

Using y  = 144 and x  =  12, we have to find the constant of proportionality.

144  =  12k

12  =  k

Therefore, y  =  12x

Substitute 7 for x.

y  =  12(7)

y  =  84

So, the value of y is 84 when x  =  7.

Problem 8 :

7 men can complete a work in 52 days. In how many days will 13 men finish the same work?

Solution :

This is a situation of inverse proportion.

Because, more men -----> less days

Let x be the no. of men and y be the no. of days.

Because this is inverse proportion, we have

y  =  k / x

Substitute 7 for x and 52 for y.

52  =  k / 7

364  =  k

Therefore,  y  =  364 / x

Substitute 13 for x.

y  =  364 / 13

y  =  28

So, 13 men can complete the work in 28 days. Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

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