. 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? [basic]
A. $3.25
B. $5.25
C. $7.75
D. $17.25
The Correct Answer and Explanation is:
To find the cost of 1 slice of cheese pizza and 3 sodas, we first define the variables:
- Let x = cost of one slice of cheese pizza
- Let y = cost of one soda
Step 1: Set up the equations
We are given two purchases:
- Richard bought 3 slices of pizza and 2 sodas for \$8.75:
$$
3x + 2y = 8.75 \quad \text{(Equation 1)}
$$
- Jordan bought 2 slices of pizza and 4 sodas for \$8.50:
$$
2x + 4y = 8.50 \quad \text{(Equation 2)}
$$
Step 2: Solve the system of equations
Let’s simplify Equation 2 by dividing all terms by 2:
$$
x + 2y = 4.25 \quad \text{(Equation 3)}
$$
Now subtract Equation 3 from Equation 1:
$$
(3x + 2y) – (x + 2y) = 8.75 – 4.25 \
(3x – x) + (2y – 2y) = 4.50 \
2x = 4.50 \
x = 2.25
$$
Now substitute x = 2.25 into Equation 3:
$$
2.25 + 2y = 4.25 \
2y = 2.00 \
y = 1.00
$$
So:
- One slice of pizza costs \$2.25
- One soda costs \$1.00
Step 3: Calculate the cost of 1 slice of pizza and 3 sodas
$$
1x + 3y = 2.25 + 3(1.00) = 2.25 + 3.00 = \boxed{5.25}
$$
Final Answer:
B. \$5.25
Explanation Summary:
This problem involves solving a system of linear equations with two variables. We translated the real-world purchases into algebraic expressions, simplified the equations, and used substitution to find the value of each item. Finally, we calculated the requested combination using the solved values. This type of algebra problem is common in real-life budgeting scenarios and reinforces the importance of translating word problems into mathematical equations accurately.