Richard bought 3 slices of cheese pizza and 2 sodas for $8.75. Jordan bought 2 slices of cheese pizza and 4 sodas for $8.50. How much would an order of 1 slice of cheese pizza and 3 sodas cost?
A. $3.25
B. $5.25
C. $7.75
D. $7.25
The Correct Answer and Explanation is:
The Correct Answer: B. $5.25
To determine how much an order of 1 slice of cheese pizza and 3 sodas would cost, we can set up a system of equations based on the purchases made by Richard and Jordan.
Let’s define the variables:
- Let ( p ) be the price of one slice of cheese pizza.
- Let ( s ) be the price of one soda.
From the information provided, we can set up the following equations:
- Richard’s purchase:
[
3p + 2s = 8.75
] - Jordan’s purchase:
[
2p + 4s = 8.50
]
Step 1: Solve the system of equations
To eliminate one of the variables, we can manipulate the equations. Let’s multiply the first equation by 2 to align the coefficients of ( s ):
[
2(3p + 2s) = 2(8.75)
]
This simplifies to:
[
6p + 4s = 17.50 \quad \text{(Equation 3)}
]
Now, we have:
- Equation 3: ( 6p + 4s = 17.50 )
- Equation 2: ( 2p + 4s = 8.50 )
Next, we can subtract Equation 2 from Equation 3:
[
(6p + 4s) – (2p + 4s) = 17.50 – 8.50
]
This simplifies to:
[
4p = 9.00
]
Dividing both sides by 4 gives us:
[
p = 2.25
]
Step 2: Substitute to find ( s )
Now that we have ( p ), we can substitute it back into either original equation to find ( s ). Let’s use the first equation:
[
3(2.25) + 2s = 8.75
]
This simplifies to:
[
6.75 + 2s = 8.75
]
Subtracting 6.75 from both sides yields:
[
2s = 2.00
]
Dividing by 2 gives:
[
s = 1.00
]
Step 3: Calculate the cost of 1 slice of pizza and 3 sodas
Now, we can calculate the total cost for 1 slice of cheese pizza and 3 sodas:
[
\text{Total cost} = 1p + 3s = 1(2.25) + 3(1.00) = 2.25 + 3.00 = 5.25
]
Thus, the cost of an order of 1 slice of cheese pizza and 3 sodas is $5.25.