At a carry-out pizza restaurant, an order of 3 slices of pizza, 4 breadsticks, and 2 juice drinks costs $13.35. A second order of 5 slices of pizza, 2 breadsticks, and 3 juice drinks cost $19.50. If four breadsticks and a juice drink cost $.30 more than a slice of pizza, what is the cost of each item?
Answers
For our ease, let's give the cost of the food items a variable name.
- Cost of one slice of pizza = p
- Cost of one breadstick = b
- Cost of one juice drink = j
(NOTE: The variables stand for the cost, not the quantity)
An order of 3 slices of pizza, 4 breadsticks & 2 juice drinks costs $13.35
➝ 3 slices of pizza + 4 breadsticks + 2 juice drinks = $13.35
➝ 3p + 4b + 2j = 13.35 ⇾ Eq(1)
An order of 5 slices of pizza, 2 breadsticks & 3 juice drinks costs $19.50.
➝ 5 slices of pizza + 2 breadsticks + 3 juice drinks = 19.50
➝ 5p + 2b + 3j = 19.50 ⇾ Eq(2)
ATQ, 4 breadsticks & 1 juice drink cost $0.30 more than a slice of pizza.
With this information, we can form another equation.
➝ 4 breadsticks + 1 juice drink = Cost of one slice of pizza + 0.30
➝ 4b + j = p + 0.30
➝ 4b + j - 0.30 = p
➝ -p + 4b + j = 0.30 ⇾ Eq(3)
⇔ Multiply Eq(3) by 5 ➝ -5p + 20b + 5j = 1.5 ⇾ Eq(4)
⇔ Multiply Eq(3) by 3 ➝ -3p + 12b + 3j = 0.9 ⇾ Eq(5)
Adding Eq(2) and Eq(4) we get:
➝ 5p + 2b + 3j - 5p + 20b + 5j = 19.50 + 1.5
➝ 2b + 3j + 20b + 5j = 21
➝ 22b + 8j = 21 ⇾ Eq(6)
Adding Eq(1) and Eq(5) we get:
➝ 3p + 4b + 2j - 3p + 12b + 3j = 13.35 + 0.9
➝ 4b + 2j + 12b + 3j = 14.25
➝ 16b + 5j = 14.25 ⇾ Eq(7)
⇔ Multiply Eq(6) by 5 ➝ 110b + 40j = 105 ⇾ Eq(8)
⇔ Multiply Eq(7) by 8 ➝ 128b + 40j = 114 ⇾ Eq(9)
Subtract Eq(8) from Eq(9).
➝ 128b + 40j - (110b + 40j) = 114 - 105
➝ 128b + 40j - 110b - 40j = 9
➝ 128b - 110b = 9
➝ 18b = 9
➝ b = 9/18
➝ b = 0.5
Substitute the value of "b" in Eq(8).
➝ 110b + 40j = 105
➝ 110(0.5) + 40j = 105
➝ 55 + 40j = 105
➝ 40j = 105 - 55
➝ 40j = 50
➝ j = 50/40
➝ j = 1.25
Now, substitute the value of "b" and "j" in Eq(1)
➝ 3p + 4b + 2j = 13.35
➝ 3p + 4(0.5) + 2(1.25) = 13.35
➝ 3p + 2 + 2.5 = 13.35
➝ 3p + 4.5 = 13.35
➝ 3p = 13.35 - 4.5
➝ 3p = 8.85
➝ p = 8.85/3
➝ p = 2.95
Final answers:
Cost of one slice of pizza = p = $2.95
Cost of one breadstick = b = $0.5
Cost of one juice drink = j = $1.25
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One way of solving such questions.
- When you're solving three equations with three unknown values, Lets say x, y and z, first, try to eliminate one of the three unknown values, say we've eliminated x.
- Then you'll get two equations with two unknowns, say, y and z. Solve both of these equations and you'll get the value of the two unknowns, i,e, y and z.
- Substitute the values of the two unknowns (y ans z) in one of the three original equations, and you'll get the value of x.
- Hence, solved.
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