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. whay is the cost of one slice of mushroom pizza?
let cost of cheese pizza be x
let cost of mushr. pizza be y
solve
3x + 4y = 1250 and
3x + 2y = 850
hint: subtract the 2nd from the 1st equation
To find the cost of one slice of mushroom pizza, we can set up a system of equations based on the given information.
Let's assign variables:
Let the cost of one slice of cheese pizza be C.
Let the cost of one slice of mushroom pizza be M.
From the first sentence, we know that Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza for a total cost of $12.50. Therefore, we can write the equation:
3C + 4M = 12.50 -- Eq. 1
From the second sentence, we know that Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. Therefore, we can write the equation:
3C + 2M = 8.50 -- Eq. 2
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.
First, isolate C in Eq. 2:
3C = 8.50 - 2M
C = (8.50 - 2M) / 3
Replace C in Eq. 1 with the value of C from Eq. 2:
3((8.50 - 2M) / 3) + 4M = 12.50
Simplifying:
8.50 - 2M + 4M = 12.50
2M = 12.50 - 8.50
2M = 4
Divide both sides by 2 to solve for M:
M = 4 / 2
M = 2
Therefore, the cost of one slice of mushroom pizza is $2.