Question

On his birthday, Manoj planned that this time he celebrates his birthday in a small orphanage centre. He bought apples to give to children and adults working there. Manoj donated 2 apples to each children and 3 apples to each adult working there along with Birthday cake. He distributed 60 total apples. a) How to represent the above situation in linear equations in two variables by taking the number of children as ‘x’ and the number of adults as ‘y’? i) 2x + y = 60 iii) 2x + 3y = 60 ii) 3x + 2y = 60 iv) 3x + y = 60 b) If the number of children is 15 then find number of adults? i) 10 iii) 15 ii) 25 iv) 20 c) If the number of adults is 12, then find the number of children? i) 12 iii) 15 ii) 14 iv) 18 d) Find the value of b, if x = 5 , y = 0 is a solution of the equation 3x + 5y = b. i) 12 iii) 15 ii) 14 iv) 18 e) Which is the standard form of linear equations in two variables: y +x = -5? i) 1(y) – 1(x) – 5 = 0 iii) 1(x) – 1(y) + 5 = 0 ii) 1(x) + 0(y) + 5 = 0 iv) 1(x) + 1(y) +5 = 0​

Answer 1

Answer:

1.2x+3y=60

2.2x+3y=60

then 2(15)+3y=60

30+3y=60

3y=60-30

3y=30

y=30/3=10 so number of adults is equal to 10

3. 2 X + 3 Y=60

2x + 3 (12)=60

2x + 36 =60

2x =60-36=24

x=24/2=12so no of childrens equal to 12

4.3(5)+5(0)=b

15+0=b

15=b

5. y-x=5

1x-1y=+5

1x-1y-5=0

option d is correct

Answer 2

The equation for the given situation is 2x + 3y = 60.

If the number of children is 15 then the number of adults is 10.

If the number of adults is 12, then the number of children is 12.

The value of b, for x = 5 , y = 0 in the equation 3x + 5y = b is 15.

The standard form of linear equations in two variables is 1(x) + 1(y) +5 = 0​.

Given:

No. of apples donated to each child= 2

No. of apples donated to each adult= 3

Total number of apples distributed= 60

To find:

The equation for the given situation.

The number of adults if the number of children is 15.

Then the number of children if the number of adults is 12.

The value of b, for x = 5 , y = 0 in the equation 3x + 5y = b.

The standard form of linear equations in two variables.

Solution:

• Linear equation is an equation in which the highest degree or highest power of the variable is one.
• Linear equation in two variables is an equation in which there are two variables of highest degree one.
• Linear equation in two variable are written in the form of ax+by+c=0.

Let x be the  number of children and y be the the number of adults.

So, the equation will be 2x + 3y = 60.           .........................(1)

If the number of children= x= 15

Put the value of x in equation 1.

2(15) + 3y = 60

30+3y=60

3y= 30

y= 30/3

y= 10

So, the number of adults is 10 only if the number of children is 15.

If the number of adults=y= 12

Put the value of y in equation 1.

2x + 3(12) = 60

2x+36=60

2x= 24

x= 24/2

x= 12

So, the number of children is 12 only if the number of adults is 12.

3x + 5y = b            .....................................(2)        

Put, x = 5 , y = 0 in equation 2.

3(5) + 5(0) = b

15+0=b

b= 15

Thus, the value of b is 15 for x = 5 , y = 0 in equation 3x + 5y = b.

The standard form of linear equations in two variables is ax+by+c=0.

Here, 1(x) + 1(y) +5 = 0​ is the standard form of linear equations in two variables.

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