Swiss cheese and Limburger cheese cost different amounts per pound, but you do not know how much. A box containing 3 pounds of Swiss and 2 pounds of limburger costs 24.40 dollar. Another box containing 4 pounds of Swiss and 5 pounds of Limburger costs 47.70 dollars. Assuming that these figures are for the cheese only (not for the box), how much does the Swiss cheese cost per pound?
3S + 2L = 24.40
4S + 5L = 47.70
Multiply the first equation by 5 and the second by 2.
15S + 10L = 122
8S + 10L = 95.40
Subtract the second equation from the first.
7S = 26.60
Divide both sides by 7.
If the costs are L and S, then we are told that
3S+2L = 24.40
4S+5L = 47.70
or,
15S+10L = 122.00
8S+10L = 95.40
subtract and you get
7S = 26.60
S = 3.80
This seems for comfortable than direct substitution.
3S+2L = 24.40, so
L = 12.20 - 1.5S
4S+5L = 47.70
4S+5(12.20-1.5S) = 47.70
-3.5S = -13.30
S = 3.80
Well, cheese Louise! This sounds like a cheesy math problem! Let's put our thinking caps on and solve it... with a little bit of humor, of course!
Let's say the cost of Swiss cheese per pound is "x," and the cost of Limburger cheese per pound is "y." Now, using our riddle-solving skills, we can create two equations.
Equation 1: 3x + 2y = 24.40
Equation 2: 4x + 5y = 47.70
We could solve these equations using some complex mathematical techniques, but who needs that when we have good old humor on our side?
Let's use some cheese-related jokes to lighten the math mood:
Why did the Swiss cheese go on vacation? Because it needed to take a slice of life!
Why was the Limburger cheese always angry? Because it had too many holes in its plans!
Now that we've laughed a bit, let's get back to solving the problem. By rearranging equation 1, we get:
2y = 24.40 - 3x
And rearranging equation 2, we get:
5y = 47.70 - 4x
Now, let's multiply equation 1 by 5 and equation 2 by 2 to eliminate the "y" variable:
10y = 122 - 15x
10y = 95.40 - 8x
Since both equations equal to 10y, we can set them equal to each other:
122 - 15x = 95.40 - 8x
Now, we can solve for "x", the cost of Swiss cheese per pound:
7x = 26.60
x = 26.60 / 7
After cranking through the numbers, we find that the cost of Swiss cheese per pound is approximately $3.80.
So, there you have it! The Swiss cheese costs around $3.80 per pound. Keep the laughs and cheese coming!
To find out how much the Swiss cheese costs per pound, we can set up a system of equations based on the given information.
Let's assume that the cost of Swiss cheese per pound is S dollars, and the cost of Limburger cheese per pound is L dollars.
From the first box, we know that the total cost of 3 pounds of Swiss cheese and 2 pounds of Limburger cheese is $24.40. This can be represented as:
3S + 2L = 24.40 -- Equation 1
Similarly, from the second box, we know that the total cost of 4 pounds of Swiss cheese and 5 pounds of Limburger cheese is $47.70. This can be represented as:
4S + 5L = 47.70 -- Equation 2
Now, we have a system of two equations with two variables.
To solve this system of equations, we can use a method called substitution or elimination. In this case, let's use the elimination method:
Multiply Equation 1 by 4 and Equation 2 by 3 to eliminate the S term:
12S + 8L = 97.60 -- Equation 3
12S + 15L = 143.10 -- Equation 4
Subtract Equation 3 from Equation 4 to eliminate the S term:
12S + 15L - (12S + 8L) = 143.10 - 97.60
7L = 45.50
Divide both sides of the equation by 7:
L = 45.50 / 7
L ≈ 6.50
Now, substitute the value of L in Equation 1 to find the value of S:
3S + 2(6.50) = 24.40
3S + 13 = 24.40
3S = 24.40 - 13
3S = 11.40
Divide both sides of the equation by 3:
S = 11.40 / 3
S ≈ 3.80
Therefore, the Swiss cheese costs approximately $3.80 per pound.