two pair of shoes and four pairs of sock cost 109,and three pairs of shoes and five pairs of socks cost 160 .Find the cost of pair of the sock
Let the shoe be=p
and the sock=q
2p+4q=109...first statement
3p+5q=160....second statement
..........
(2p+4q=109)3
(3p+5q=160)2
6p+12q=327
6p+10q=320
...................
-2q=-7
q=3.5
Well, it seems the shoes and the socks are quite the dynamic duo here, causing some pricing mischief. Let's examine this puzzle.
Let's assume the cost of a pair of shoes is "S" and the cost of a pair of socks is "K".
According to the information given,
2S + 4K = 109 ---(Equation 1)
3S + 5K = 160 ---(Equation 2)
Now, we have two equations and two unknowns. Let's put our funny math hats on and solve this.
Multiply Equation 1 by 3 and Equation 2 by 2 to make the coefficients of S the same:
6S + 12K = 327 ---(Equation 1, multiplied by 3)
6S + 10K = 320 ---(Equation 2, multiplied by 2)
Now, subtract Equation 2 from Equation 1:
(6S + 12K) - (6S + 10K) = 327 - 320
2K = 7
Divide both sides by 2 to solve for K:
K = 7/2
So, a pair of socks costs 7/2 or in other words, it costs 3.50.
So, the cost of a pair of socks is $3.50. But hey, don't let the socks hog all the limelight! The shoes deserve their comedy routine too!
Let's assume the cost of a pair of shoes is 'x' and the cost of a pair of socks is 'y'.
From the given information, we have two equations:
Equation 1: 2x + 4y = 109
Equation 2: 3x + 5y = 160
We can solve these equations simultaneously to find the values of 'x' and 'y'.
Step 1: Multiply Equation 1 by 3 and Equation 2 by 2 to eliminate the 'x' variable.
6x + 12y = 327
6x + 10y = 320
Step 2: Subtract Equation 2 from Equation 1 to eliminate the 'x' variable.
(6x - 6x) + (12y - 10y) = 327 - 320
2y = 7
Step 3: Solve for 'y' by dividing both sides of the equation by 2.
y = 7/2
y = 3.5
The cost of a pair of socks is 3.5.
To find the cost of a pair of socks, we can set up a system of equations.
Let's call the cost of one pair of shoes "x" and the cost of one pair of socks "y".
According to the problem:
Two pairs of shoes and four pairs of socks cost 109. This can be represented as:
2x + 4y = 109 Equation 1
Three pairs of shoes and five pairs of socks cost 160. This can be represented as:
3x + 5y = 160 Equation 2
Now, we have a system of equations. We can solve this system to find the values of x and y.
Multiplying Equation 1 by 3 and Equation 2 by 2, we can eliminate x and solve for y:
(3)(2x + 4y) = (3)(109) Simplifying,
6x + 12y = 327 Equation 3
(2)(3x + 5y) = (2)(160) Simplifying,
6x + 10y = 320 Equation 4
Subtracting Equation 4 from Equation 3 to eliminate x:
(6x + 12y) - (6x + 10y) = 327 - 320
2y = 7
Dividing by 2 on both sides:
y = 7/2
So, the cost of one pair of socks is 7/2, or $3.50.