Question

instructions
solve the following problem and select your answer from the choices given.

question

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?

$3.25

$5.25

$7.75

$17.25

Explanation:

Step1: Define variables

Let \( p \) be the price of one slice of pizza and \( s \) be the price of one soda.
We have the following equations:
\( 3p + 2s = 8.75 \) (from Richard's purchase)
\( 2p + 4s = 8.50 \) (from Jordan's purchase)

Step2: Simplify the second equation

Divide the second equation \( 2p + 4s = 8.50 \) by 2:
\( p + 2s = 4.25 \)

Step3: Subtract the simplified equation from the first

Subtract \( p + 2s = 4.25 \) from \( 3p + 2s = 8.75 \):
\( (3p + 2s) - (p + 2s) = 8.75 - 4.25 \)
\( 2p = 4.5 \)
\( p = 2.25 \)

Step4: Find the price of a soda

Substitute \( p = 2.25 \) into \( p + 2s = 4.25 \):
\( 2.25 + 2s = 4.25 \)
\( 2s = 4.25 - 2.25 \)
\( 2s = 2 \)
\( s = 1 \)

Step5: Calculate the cost of 1 pizza and 3 sodas

The cost is \( p + 3s \). Substitute \( p = 2.25 \) and \( s = 1 \):
\( 2.25 + 3\times1 = 2.25 + 3 = 5.25 \)

Answer:

\$5.25