Answer: Pizza = $2.95, Breadstick = $0.50, Juice = $1.25
Step-by-step explanation:
Let P represent the cost of a slice of pizza
and B represent the cost of breadstick
and J represent the cost of a juice drink.
EQ1: 3P + 4B + 2J = 13.35
EQ2: 5P + 2B + 3J = 19.50
EQ3: 4B + J = P + 0.30 --> P - 4B - J = -0.30
Let's eliminate B from EQ1 and EQ2 to form EQ4:
3P + 4B + 2J = 13.35 → 1(3P + 4B + 2J = 13.35) → 3P + 4B + 2J = 13.35
5P + 2B + 3J = 19.50 → -2(5P + 2B + 3J = 19.50) → -10P - 4B - 6J = -39.00
EQ4: -7P -4J = -25.65
And eliminate B from EQ1 and EQ3 to form EQ5:
3P + 4B + 2J = 13.35
P - 4B - J = -0.30
EQ5: 4P + J = 13.05
Now, eliminate J from EQ4 and EQ5 to solve for P:
-7P - 4J = -25.65 → 1(-7P - 4J = -25.65) → -7P - 4J = -25.65
4P + J = 13.05 → 4(4P + J = 13.05) → 16P +4J = 52.20
9P = 26.55
÷9 ÷9
P = 2.95
Plug in P = 2.95 into EQ4 or EQ5 to solve for J:
EQ5: 4P + J = 13.05
4(2.95) + J = 13.05
11.80 + J = 13.05
J = 1.25
Plug in P = 2.95 and J = 1.25 into either EQ1 or EQ2 or EQ3 to solve for B:
EQ3: 4B + J = P + 0.30
4B + 1.25 = 2.95 + 0.30
4B + 1.25 = 3.25
4B = 2.00
B = 0.50
Check (since we used EQ3 to find B, use either EQ1 or EQ2):
EQ2: 5P + 2B + 3J = 19.50
5(2.95) + 2(0.50) + 3(1.25) = 19.50
14.75 + 1.00 + 3.75 = 19.50
19.50 = 19.50 [tex]\checkmark[/tex]
