At a concession stand three hot and 4 hamburgers cost 13.50; 4 hot dogs and 3 numbers cost 12.75. Find the cost one hot dog and the cost of one hamburger
x = the cost of hot dog
y = the cost of hamburger
3 x + 4 y = 13.5
4 x + 3 y = 12.75
3 x + 4 y = 13.5
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4 x + 3 y = 12.75
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- x + y = 0.75 Add x to both sides
- x + y + x = 0.75 + x
y = 0.75 + x
4 x + 3 y = 12.75
4 x + 3 * ( 0.75 + x ) = 12.75
4 x + 2.25 + 3 x = 12.75
7 x + 2.25 = 12.75 Subtract 2.25 to both sides
7 x + 2.25 - 2.25 = 12.75 - 2.25
7 x = 10.5 Divide both sides by 7
x = 10.5 / 7 = 1.5
y = 0.75 + x = 1.5 + 0.75 = 2.25
the cost of hot dog = 1.5
the cost of hot hamburger = 2.25
Well, these hot dogs and hamburgers are making quite a deal. They seem more affordable than a therapy session with a clown. Let me crunch some numbers for you:
Let's assume the cost of one hot dog is "h" and the cost of one hamburger is "b".
From the given information, we have the first equation:
3h + 4b = 13.50
And the second equation:
4h + 3b = 12.75
Now, let's solve this puzzle using some math magic!
Multiplying the first equation by 4, we have:
12h + 16b = 54
Multiplying the second equation by 3, we get:
12h + 9b = 38.25
Now, we have a system of equations:
12h + 16b = 54
12h + 9b = 38.25
Subtracting the second equation from the first equation, we can eliminate the h term:
(12h + 16b) - (12h + 9b) = 54 - 38.25
7b = 15.75
Dividing both sides by 7, we find:
b = 2.25
Now, to find the cost of one hot dog, let's substitute the value of b into either of the original equations. Let's choose the first one:
3h + 4(2.25) = 13.50
3h + 9 = 13.50
3h = 13.50 - 9
3h = 4.50
h = 1.50
So, the cost of one hot dog is $1.50, and the cost of one hamburger is $2.25.
Remember, with the money you save from this deal, you can buy yourself a clown nose and a wig!
Let's assume the cost of one hot dog is "x" dollars and the cost of one hamburger is "y" dollars.
According to the given information, we can form two equations:
Equation 1: 3x + 4y = 13.50
Equation 2: 4x + 3y = 12.75
We can solve these equations simultaneously to find the values of x and y.
Multiplying equation 1 by 4 and equation 2 by 3 to eliminate "y", we get:
12x + 16y = 54
12x + 9y = 38.25
Subtracting equation 2 from equation 1:
(12x + 16y) - (12x + 9y) = 54 - 38.25
7y = 15.75
Dividing both sides by 7:
y = 15.75 / 7
y ≈ 2.25
So, the cost of one hamburger is approximately $2.25.
Substituting this value back into equation 1:
3x + 4(2.25) = 13.50
3x + 9 = 13.50
3x = 13.50 - 9
3x = 4.50
Dividing both sides by 3:
x = 4.50 / 3
x = 1.50
Therefore, the cost of one hot dog is $1.50.
To find the cost of one hot dog and one hamburger, we can set up a system of equations based on the information given.
Let's assume the cost of one hot dog is 'x' and the cost of one hamburger is 'y'.
From the first sentence, we have the equation:
3x + 4y = 13.50
From the second sentence, we have the equation:
4x + 3y = 12.75
We can solve this system by using the method of substitution or elimination. Let's use the method of elimination to eliminate one variable.
Multiply the first equation by 4, and the second equation by 3 to make the coefficients of the x terms the same:
12x + 16y = 54
12x + 9y = 38.25
Now, subtract the second equation from the first equation:
(12x + 16y) - (12x + 9y) = 54 - 38.25
12x + 16y - 12x - 9y = 15.75
7y = 15.75
Divide both sides of the equation by 7 to solve for y:
y = 15.75 / 7
y ≈ 2.25
Now, substitute the value of y into one of the original equations to solve for x. Let's use the first equation:
3x + 4(2.25) = 13.50
3x + 9 = 13.50
3x = 13.50 - 9
3x = 4.50
Divide both sides of the equation by 3 to solve for x:
x = 4.50 / 3
x = 1.50
Therefore, the cost of one hot dog is approximately $1.50, and the cost of one hamburger is approximately $2.25.