SIMPLIFYING RATIONAL EXPRESSIONS WORD PROBLEMS
Problem 1 :
Pari needs 4 hours to complete a work. His friend Yuvan needs 6 hours to complete the same work. How long will it take to complete if they work together?
Solution :
Number of hours taken by pari = 4 hours
Number of hours taken by Yuvan = 6 hours
Work done in one hour by Pari = 1/4
Work done in one hour by Pari = 1/6
work done by together in one hour = (1/4) + (1/6)
= (6 + 4)/4(6)
= 10 / 24
= 5/12
Number of hours taken by both = 12/5
Let us convert into minutes = (12/5) 60 = 144 minutes
= 2 hours 24 minutes.
Problem 2 :
Iniya bought 50 kg of fruits consisting of apples and bananas. She paid twice as much per kg for the apple as she did for the banana. If Iniya bought ₹ 1800 worth of apples and ₹ 600 worth bananas, then how many kgs of each fruit did she buy?
Solution :
Let "x" be number of kgs of banana and "2x" be the number of kgs of apple.
Cost of apple = 1800
Number of kgs of apple (cost per kg) = 1800
Number of kgs of apple (2x) = 1800
Number of kgs of apple = 1800/2x = 900/x -----(1)
Number of kgs of banana (cost per kg) = 600
Number of kgs of banana (x) = 600
Number of kgs of apple = 600/x -----(2)
(1) + (2)
(900/x) + (600/x) = 50
(1500 / x) = 50
x = 1500/50
x = 30
By applying x = 30 in (1), we get
Number of kgs of apple = 1800/2(30) = 30
By applying x = 30 in (2), we get
Number of kgs of banana = 600/30 = 20
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