Solving for ₹2 and ₹5 Coins
Let the number of ₹2 coins be '$x$' and the number of ₹5 coins be '$y$'.
Formulating Equations
We are given two conditions:
- Total number of coins: $x + y = 60$
- Total amount of money: $2x + 5y = 240$
Calculating Coin Counts
We can solve this system of linear equations. From the first equation, express '$x$' in terms of '$y$':
$x = 60 - y$
Substitute this expression for '$x$' into the second equation:
$2(60 - y) + 5y = 240$
Simplify and solve for '$y$':
$120 - 2y + 5y = 240$
$120 + 3y = 240$
$3y = 240 - 120$
$3y = 120$
$y = \frac{120}{3}$
$y = 40$
Now substitute the value of '$y$' back into the equation for '$x$':
$x = 60 - 40$
$x = 20$
Verifying the Solution
Check if the calculated values satisfy the original conditions:
- Total coins: $20 + 40 = 60$ (Matches)
- Total amount: $(2 \times 20) + (5 \times 40) = 40 + 200 = 240$ (Matches)
Thus, Rakesh has 20 coins of ₹2 and 40 coins of ₹5.
Similar Questions
- The cost of 7 pens and 8 pencils is ₹230. If the cost of a pen decreases by ₹1 and the cost of a pencil increases by ₹7, then the cost of 14 pens and 4 pencils is ₹150. What is the original cost of 8 pens and 8 pencils?
- The cost of 2 pens and 15 pencils is ₹286. If the cost of a pen decreases by ₹4 and the cost of a pencil increases by ₹2, then the cost of 17 pens and 3 pencils is ₹128. What is the original cost of 11 pens and 8 pencils?
- The electricity bill of a certain establishment is partly fixed and partly variable depending on the number of units of electricity consumed. In a certain month when 540 units were consumed, the bill was ₹1,800. In another month when 620 units were consumed, the bill was ₹2,040. If in a month 500 units are consumed, then the bill for that month will be:
- The cost of 10 pencils and 12 pens is ₹150. What is the cost of 30 pencils and 36 pens?
- If 33 is the sum of two numbers and 13 is their difference, then find the largest number.
- 2 chairs and 1 table cost ₹880, while 1 chair and 2 tables cost ₹980. Find the cost of each.
- If $2x - 3y = 7$ and $\frac{x}{x+y} = \frac{5}{6}$, then what is the value of $x - y$?
If $2x - 3y = -1$ and $\frac{x}{x+y} = \frac{7}{12}$, then the value of $2xy$ is:
- If the system of equation $3x - 2y = 8$, $2ax + (a-b)y = 48$ has infinitely many solutions then:
- If $2x + 3y = 23$ and $x = 4$, then what is the value of $y$?
Important Questions from Linear Equation in 2 Variable
What is the solution of the following equations ?
2x + 3y = 12 and 3x − 2y = 5
Two positive numbers differ by 1280. When the greater number is divided by the smaller number, the quotient is 7 and the remainder is 50. The greater number is:
When 5 children from class A join class B, the number of children in both classes is the same. If 25 children from B, join A, then the number of children in A becomes double the number of children in B. The ratio of the number of children in A to those in B is:
If (x + 6y) = 8, and xy = 2, where x > 0, what is the value of (x 3+ 216y 3)?
If 8k 6+ 15k 3– 2 = 0, then the positive value of \(\left( {{\rm{k}}\,{\rm{ + }}\,\frac{1}{{\rm{k}}}} \right)\) is :
