A sandwich store charges $4.50 for each sandwich and a $10 delivery fee. An office pays $82 to have sandwiches delivered for their employees. How many sandwiches did they order?

Let each turkey sandwich cost x, and the fixed delivery fee be y.

From the first situation, 4x + y = 33

From the second case with 8 sandwiches, 8x + y = 61

Subtracting the first equation from the second gives 4x = 28

x = 7

Substituting this back into the first equation gives y = 5.

Therefore, each turkey sandwich costs $7 and the delivery fee is $5.

If you were to have 12 turkey sandwiches delivered, the cost would be 12x + y = 12*7 + 5 = $89, so this would be more than $85.

If you want to do it graphically, convert both equations into slope-intercept form.

y = -4x + 33 and y = -8x + 61

For the first equation, the y-intercept is (0,33) and the x-intercept is (33/4, 0).

For the second equation, the y-intercept is (0,61) and the x-intercept is (61/8, 0).

Connect the intercepts for each equation, then find the point of intersection. The x- and y-coordinates of the point of intersection are x = 7 and y = 5, which are the values that will solve the equations.

Step-by-step explanation:

c. 1,233 miles

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9