Question

What is the total number of natural number solutions to 3X+2Y = 50 if X < Y?

a)10 b) 6 c) 4 d) 2​

Answer 1

Answer:

The answer is 10

Step-by-step explanation:

3*10+2*10=50

30+20=50

Answer 2

The total number of natural number solutions to 3X+2Y = 50 if X < Y is 4

Given :

The equation 3X + 2Y = 50 if X < Y

To find :

The total number of natural number solutions to 3X + 2Y = 50 if X < Y is

a) 10

b) 6

c) 4

d) 2

Solution :

Step 1 of 3 :

Write down the given equation

Here the given equation is

3X + 2Y = 50 if X < Y

Step 2 of 3 :

Express Y in terms of X

$\displaystyle \sf{ 3X + 2Y = 50 }$

$\displaystyle \sf{ \implies Y = \frac{50 - 3X}{2} }$

Step 3 of 3 :

Find the total number of solutions

$\displaystyle \sf{ Y = \frac{50 - 3X}{2} \: \: where \: \: X < Y}$

From the above it is obvious that X must be even natural number

For X = 2 value of Y = 22 where X < Y holds

For X = 4 value of Y = 19 where X < Y holds

For X = 6 value of Y = 16 where X < Y holds

For X = 8 value of Y = 13 where X < Y holds

For X = 10 value of Y = 10 where X < Y does not hold

So the solution set (X, Y) is given by (2,22) , (4,19) , (6,16) , (8,13)

Thus the total number of natural number solutions to 3X+2Y = 50 if X < Y is 4

Hence the correct option is c) 4

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