"Question 15 I have a total of Rs 300 in coins of denomination Re 1, Rs 2 and Rs 5. The number of Rs 2 coins is 3 times the number of Rs 5 coins. The total number of coins is 160. How many coins of each denomination are with me?
Linear Equations in One Variable Page 28"
Answers
Equations with linear expressions in one variable only are known as linear equations in one variable.
An algebraic equation is an equality involving variables. It has an equality sign(=). The expression on the left of the equality sign is the Left Hand Side (LHS). The expression on the right of the equality sign is the Right Hand Side (RHS).
In an equation the values of the expressions on the LHS and RHS are equal.
Transposition:
Any term of a equation may be taken from one side to other with the change in its sign, this does not affect the equality of the statement . This process is called transposition.
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Solution:
Let the number of ₹ 5 coins be x.
& the Number of ₹ 2 coins be 3x.
Total number of coins =160
(Given)
Number of ₹ 1 coin = 160 − (Number of coins of ₹
5 and of ₹ 2)
= 160 − (3x + x)
= 160 – 4x
Amount of ₹1 coins = ₹ [1 × (160 − 4x)]
= ₹ (160 − 4x)
Amount of ₹ 2 coins = ₹ (2 × 3x)= ₹ 6x
Amount of ₹ 5 coins = ₹ (5 × x) = ₹ 5x
A.T.Q
Total
amount is ₹ 300 (given)
(160 – 4x) + 6x + 5x = 300
160+2x+5x=300
160 + 7x =
300
Transposing 160 to R.H.S,
7x =
300 – 160
7x =
140
x= 140/7
x = 20
So , the number of coins of each denominations will be
Number of ₹1 coins = 160 – 4x
= 160 − 4 × 20
= 160 − 80 = 80
Number of ₹ 2 coins = 3x
= 3 × 20 = 60
Number of ₹ 5 coins = x
= 20
Hence, Number of ₹1 coins = 80
Number of ₹2 coins = 60
Number of ₹5 coins = 20
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Hope this will help you....
Answer:
Answer : x=80, y=60 & z=20
Step-by-step explanation:
