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 1 slice of mushroom pizza?
Let x = slices of cheese pizza and y = mushroom.
3x + 4y = 12.5
3x + 2y = 8.5
Subtract second equation from first.
2y = 4
y = 2
I hope this helps. Thanks for asking.
Let's solve the problem step by step:
Step 1: Set up equations based on the given information.
Let C represent the cost of 1 slice of cheese pizza.
Let M represent the cost of 1 slice of mushroom pizza.
From the first piece of information, we know that:
3C + 4M = 12.50 (Equation 1)
From the second piece of information, we know that:
3C + 2M = 8.50 (Equation 2)
Step 2: Solve the system of equations.
We can solve the system of equations by using substitution or elimination. In this case, we'll use the elimination method.
Multiply Equation 2 by 2 to make the coefficients of M the same for both equations:
6C + 4M = 17 (Equation 3)
Subtract Equation 1 from Equation 3 to eliminate M:
(6C + 4M) - (3C + 4M) = 17 - 12.50
6C + 4M - 3C - 4M = 4.50
3C = 4.50
Simplify the equation:
3C = 4.50
C = 4.50 / 3
C = 1.50
Step 3: Substitute the value of C into Equation 1 (or Equation 2) to find the value of M.
3C + 4M = 12.50
3(1.50) + 4M = 12.50
4.50 + 4M = 12.50
4M = 12.50 - 4.50
4M = 8
Simplify the equation:
4M = 8
M = 8 / 4
M = 2
Step 4: Answer the question.
The cost of 1 slice of mushroom pizza is $2.
Therefore, 1 slice of mushroom pizza costs $2.
To find the cost of one slice of mushroom pizza, we need to set up a system of equations based on the information given.
Let's say 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 3 slices of cheese pizza and 4 slices of mushroom pizza cost $12.50. This can be expressed as the equation:
3C + 4M = 12.50
From the second statement, we know that 3 slices of cheese pizza and 2 slices of mushroom pizza cost $8.50. This can be expressed as the equation:
3C + 2M = 8.50
Now we have a system of equations:
3C + 4M = 12.50
3C + 2M = 8.50
To solve this system, we can use the method of elimination. We'll start by eliminating the variable "C". Subtracting the second equation from the first equation, we get:
(3C + 4M) - (3C + 2M) = 12.50 - 8.50
Simplifying the equation gives us:
2M = 4
Dividing both sides of the equation by 2, we find:
M = 2
Therefore, the cost of one slice of mushroom pizza is $2.