20. 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.
HAPP
(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 the number of adults?
(i) 10
(i) 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
Answers
Answer:
a) 2x + 3y = 60
b) 10
c) 15
d) 15
Given:
Manoj celebrated his birthday in small orphanage
Manoj donated 2 apples to each children and 3 apples to each adult
Total No. of apples distributed = 60
Solution:
(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'?
⇒ No. of children is taken as x
then No. of apples gave 1 child = 2
⇒ No. of apples for x children = 2x
⇒ No. of adult is taken as y
then No. of apples gave 1 adult = 3
⇒ No. of apples for y adults = 3y
Therefore, total No. of apples = 2x+3y = 60
∴ The answer is option (iii) 2x+3y = 60
(b) If the number of children is 15. then find the number of adults?
⇒ No. of children x = 15 [ substitute the value in above equation]
⇒ 2(15)+3y = 60
⇒ 30 + 3y = 60
⇒ 3y = 30
⇒ y = 10
∴ The answer is option (i) 10
(c) If the number of adults is 12, then find the number of children?
No. of adults y = 12 [ substitute the value in equation]
⇒ 2x+3(12) = 60
⇒ 2x + 36 = 60
⇒ 2x = 24
⇒ x = 12
∴ The answer is option (i) 12
(d) Find the value of b, if x=5, y=0 is a solution of the equation 3x + 5y = b
⇒ Given x = 5 and y = 0 [ substitute in given equation ]
⇒ 3(5) + 5(0) = b
⇒ 15 = b
∴ The answer is option (iii) 15
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