Question

Please help with this!!

Answer 1

Hello!

Forming the equations :

y = mx + b

m = rate per hour

b = fixed charge

`\fbox {y = 15x + 500}`

`\fbox {y = 18x + 350}`

Solving for number of guests at which cost is the same :

15x + 500 = 18x + 350

3x = 150

x = 25 guests

Answer 2

Explanation:

Forming linear equations and solving:

Cost = fixed rate + number of guests* cost per meal.

Let x be the number of guests.

a) Pin hall:

Fixed rate = $ 500

Cost per meal = $15

Cost = 500 + 15*x

`\sf \boxed{\bf C = 500 + 15x}`

Bloom place:

Fixed rate = $350

Cost per meal = $18

`\sf \boxed{\bf C = 350 +18x}`

b) Given the charges are same at both halls.

350 + 18x = 500 + 15x

18x = 500 + 15x - 350

18x = 150 + 15x

18x -15x = 150

3x = 150

x = 150 ÷ 3

x = 50

When the number of guests is 50, the cost is same at both the halls