At the end of the day of teaching the skill of cutting and sewing to make capes, Ms. Ironperson and Mr. Thoro decided to go to the Shawarma Mediterranean Grill. Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95. Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91. What is the cost of a chicken shawarma wrap? What is the cost of one order of spiced potatoes?

a) Cost of a chicken shawarma wrap?

$10.99

b) Cost of one order of spiced potatoes?

$4.99

Step-by-step explanation:

Cost of a chicken sharwarma wrap = a

Cost of an order of spiced potatoes = b

Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95.

3a + 2b = $42.95 Equation 1

Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91.

5a + 4b = $74.91 Equation 2

So we have:

3a + 2b = $42.95 Equation 1

5a + 4b = $74.91 Equation 2

We use Elimination method to solve for this.

Multiply Equation 1 by coefficient of b in Equation 2

Equation 2 by coefficient of b in Equation 1

3a + 2b= $42.95 Equation 1 × 4

5a + 4b = $74.91 Equation 2 × 2

12a + 8b = 171.80Equation 3

10a + 8b = 149.82Equation 4

Subtract Equation 3 from Equation 4

2a = 21.98

a = 21.98/2

a = 10.99

Therefore, a = Cost of Chicken sharwarma wrap = $10.99

Subtitute 10.99 for 9in Equation 1

3a + 2b = $42.95 Equation 1

3(10.99) + 2b = 42.95

32.97 + 2b = 42.95

2b = 42.95 - 32.97

2b = 9.98

b = 9.98/2

b = 4.99

b = Cost of an order of spiced potatoes = $4.99

Hence,

The cost of a chicken sharwarma wrap = $10.99

The cost of an order of spiced potatoes = $4.99

step-by-step explanation:

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.