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Three liner equation problems for practice

Question 1
Green and blue coloured toys are 149 in number in a box. Two green toys are removed from the lot and now there are twice as many green ones as blue ones. How many green coloured toys are there now?
a) 76 b) 86 c) 90 d) 98
Answer : d) 98
Solution:
Let x and y be the original number of green and blue toys respectively. Originally there were 149 toys. Hence,
x + y = 149 ----------(1)
After two green toys were removed, the number of green toys becomes twice that of the blue toys.
x-2 = 2 y -----------(2)
Solving eq 1 and eq 2 we get
3 y = 149-2=147
y= 49
Current number of green toys (after removal of two) is twice as that of blue ones.So the green toys are 98 in number.
Question 2
Roushan was a B.E student pursuing studies in the city of Vizag. During summer holidays he visited his village.In the courtyard of his house, there are many hens and goats. Roushan asked his sister as to how many hens are there in the courtyard. His sister who is a village girl gave her reply like this : If you count all the heads you will get 300. But if you count the legs you will get 700. Can you help Roushan in calculating the number of hens.
(a) 200 (b) 250 (c) 600 (d) 400
Answer : b) 250
Solution:
Let us assume that x number of hens and y number of goats are there in the courtyard.
x+y = 300, -------(1) since the total head count is given as 300.
Its given, there are totally 700 legs when counted. We know the hens have two legs and the goats have 4 legs. Therefore
2x+4y= 700 -------(2)
(1)x2 will give, 2x+2y=600 -------(3)
(2)-(3) will give you, 2y=100 and y=50.
Substituting in equation (1) you get x value as 250
Question 3
Average age of three brothers is 5. Youngest brother thinks, "If I had born earlier along with the middle brother, I would be just short of 8 years compared to my eldest brother". Middle brother thinks, "If I had born later along with my younger brother, I would be short of 10 years compared to my eldest brother." What is the age of middle brother ?
a) 3 years b) 1 year c) 2 years d) 4 years
Answer : a) 3 years.
Solution :
Let x,y and z be the ages of youngest, middle and eldest brother.
The average of their ages is 5. i,e x + y + z / 3 = 5 Or x + y + z = 15 ...(1)
Youngest brother thinks that If he had born earlier along with his middle brother he would be just short of 8 years compared to his eldest brother.
This statement implies that if youngest brother had the age of his middle brother he would be short of 8 years compared to his eldest brother. This indirectly implies that middle brother is short of eldest brother by 8 years.
i.e z - y = 8 ...(2)
Similarly the middle brother thinks if he was as old as his youngest brother he would be short of 10 years compared to his eldest brother. This indirectly implies that youngest brother is 10 years lesser than eldest brother.
i.e z - x = 10 ...(3)
Adding equations 1,2 and 3, we get
3z = 33 or z = 11
Substitute z = 11 in eq 2 we get,
11 - y = 8
Or y = 3
Therefore age of middle brother is 3 years.

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