Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza for a total cost of $12.50. Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. What is the cost of one slice of mushroom pizza?
To find the cost of one slice of mushroom pizza, we need to set up a system of equations using the given information.
Let's assume the cost of one slice of cheese pizza is C dollars and the cost of one slice of mushroom pizza is M dollars.
From the first statement, we know that Jack bought 3 slices of cheese pizza (3C) and 4 slices of mushroom pizza (4M) for a total cost of $12.50:
3C + 4M = 12.50 (Equation 1)
From the second statement, we know that Grace bought 3 slices of cheese pizza (3C) and 2 slices of mushroom pizza (2M) for a total cost of $8.50:
3C + 2M = 8.50 (Equation 2)
Now we can solve this system of equations to find the value of M, the cost of one slice of mushroom pizza.
To eliminate C, we can multiply Equation 2 by 2 and Equation 1 by 3:
(2)(3C + 2M) = (2)(8.50) --> 6C + 4M = 17 (Equation 3)
(3)(3C + 4M) = (3)(12.50) --> 9C + 12M = 37.50 (Equation 4)
Next, let's multiply Equation 3 by 3 and Equation 4 by 2 to create coefficients that can be eliminated:
(3)(6C + 4M) = (3)(17) --> 18C + 12M = 51 (Equation 5)
(2)(9C + 12M) = (2)(37.50) --> 18C + 24M = 75 (Equation 6)
Subtracting Equation 5 from Equation 6 will eliminate C:
(18C + 24M) - (18C + 12M) = 75 - 51
12M = 24
M = 24/12
M = 2
Therefore, the cost of one slice of mushroom pizza is $2.
To find the cost of one slice of mushroom pizza, we can set up a system of equations using the given information.
Let's assume the cost of one slice of cheese pizza is represented by C, and the cost of one slice of mushroom pizza is represented by M.
From the first statement, we know that Jack bought 3 slices of cheese pizza at a cost of 3C, and 4 slices of mushroom pizza at a cost of 4M. The total cost for Jack is $12.50, so we can write the equation as:
3C + 4M = 12.50
Similarly, from the second statement, we know that Grace bought 3 slices of cheese pizza at a cost of 3C, and 2 slices of mushroom pizza at a cost of 2M. The total cost for Grace is $8.50, so we can write the equation as:
3C + 2M = 8.50
To solve this system of equations, we can use the method of elimination.
First, multiply the second equation by 2 to eliminate the M term:
2 * (3C + 2M) = 2 * 8.50
6C + 4M = 17
Now, subtract the first equation from the modified second equation:
(6C + 4M) - (3C + 4M) = 17 - 12.50
6C - 3C + 4M - 4M = 4.50
3C = 4.50
Divide both sides of the equation by 3 to solve for C:
C = 4.50 / 3
C = 1.50
Substitute the value of C back into either of the original equations. Let's use the first equation:
3(1.50) + 4M = 12.50
4.50 + 4M = 12.50
4M = 12.50 - 4.50
4M = 8
Divide both sides of the equation by 4 to solve for M:
M = 8 / 4
M = 2
Therefore, the cost of one slice of mushroom pizza is $2.
3C + 4M = 12.50
3C + 2M = 8.50
Subtract the second equation from the first and solve.