Question

sherin and her husband on their wedding anniversary decided to spend the time in a special school they brought chocolates to give to children and adults working there the gifted 2 chocolates to childrens and 3 chocolates to each adult working there they distributed a total of 60 chocolates

1. 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
(ii) 2x + 3y = 60
(iii) 3x + 2y = 60
(iv) 3x + y = 60
2. If the number of children is 15, then find the number of adults?
(i) 10
(ii) 15
(iii) 25
(iv) 20
3. Find the value of b, if x = 5, y = 0 is a solution of the equation 3x + 5y = b.
(i) 12
(ii) 15
(iii) 14
(iv) 18
4 Which is the standard form of linear equations in two variables: y – x = 5 ?
(i) 1.y – 1.x – 5 = 0
(ii) 1.x – 1.y + 5 = 0
(iii) 1.x + 0.y + 5 = 0
(iv) 1.x – 1.y – 5 = 0​

Answer 1

Linear Equation In Two Variables

Step-by-step explanation:

It is given that sherin and her husband gifted $2$ chocolates to each children and $3$ chocolates to each adult.

In total, they distributed $60$ chocolates.

1. Suppose the number of children be $x$ and number of adult be $y$.

They gifted $2$ chocolates to each children and $3$ chocolates to each adult.

Therefore, total number of chocolates distributed to children will be $2x$.

And, total number of chocolates distributed to adults will be $3x$.

That means,

The situation given will be represented as:

                                               $2x+3y=60$

Hence, option $(ii)$ is correct.

     2. Number of children given is $15$

Therefore, we get

                                  $2x+3y=60\\2(15)+3y=60\\30+3y=60\\3y=30\\y=10$

That means, the number of adults will be $10$.

Hence, option $(i)$ is correct.

        3.  It is given that $x=5$, $y=0$.

And, $3x+5y=b$.

Therefore, the value of $b$ will be given by

                                  $3x+5y=b\\3(5)+5(0)=b\\15+0=b\\b=15$

That means, we get that option $(ii)$ is correct.

          4. The given equation is: $y-x=5$

Therefore, the standard form of the equation in two variables will be:

                                      $y-x=5\\0=5-y+x\\x-y+5=0\\1.x-1.y+5=0$

Hence, option $(ii)$ is correct.