Carmen and hannah bought lunch at the pizza shop. Carmen ordered two slices of pizza an three cans of juice. Hannah ordered three slices of pizza and two cans of juice. Carmens bill was $5.25 and hannahs bill was $6.00. What was the price of one slice of pizza? of one can of juice?
2P + 3J = 5.25
3P + 2J = 6.00
Multiply first equations by 3 and second by 2.
6P + 9J = 15.75
6P + 4J = 12.00
Subtract second from first.
5J = 3.75
Solve for J and insert that value into either original equation to find P. To check, put both values into the other equation.
To find the price of one slice of pizza and one can of juice, we can set up a system of equations based on the given information.
Let's let x represent the price of one slice of pizza and y represent the price of one can of juice.
From the given information:
Carmen ordered 2 slices of pizza and 3 cans of juice, and her bill was $5.25.
So, 2x + 3y = 5.25. (Equation 1)
Hannah ordered 3 slices of pizza and 2 cans of juice, and her bill was $6.00.
So, 3x + 2y = 6.00. (Equation 2)
We now have a system of equations.
To find the price of one slice of pizza and one can of juice, we can solve this system of equations using either the substitution method or the elimination method. Let's use the elimination method in this case.
Multiply Equation 1 by 3 and Equation 2 by 2 to make the coefficients of x in both equations equal:
6x + 9y = 15.75 (Equation 3)
6x + 4y = 12 (Equation 4)
Now, subtract Equation 4 from Equation 3 to eliminate the x term:
(6x - 6x) + (9y - 4y) = 15.75 - 12
5y = 3.75
Divide both sides of the equation by 5 to solve for y:
y = 3.75 / 5
y = 0.75
So, the price of one can of juice is $0.75.
To find the price of one slice of pizza, substitute the value of y back into either Equation 1 or Equation 2. Let's use Equation 1:
2x + 3(0.75) = 5.25
2x + 2.25 = 5.25
Subtract 2.25 from both sides of the equation:
2x = 5.25 - 2.25
2x = 3.00
Divide both sides of the equation by 2 to solve for x:
x = 3.00 / 2
x = 1.50
So, the price of one slice of pizza is $1.50.
Therefore, the price of one slice of pizza is $1.50, and the price of one can of juice is $0.75.