Problema Solution
you are planning a reunion. You have 2 options to pay for food and the hall. 1st option, you pay $240 for the use of the hall and pay a caterer $8 per person for food. 2nd option, the banquet hall will also furnish the food for $600.
a. Write a system of equations describing the total cost of the reunion.
b. Solve the system of equations. After how many members are the options equal?
c. When does the 1st option have the lower total cost? When does the 2nd option have the lower total cost?
Answer provided by our tutors
let 'x' be the number of members coming to the reunion
a. Write a system of equations describing the total cost of the reunion.
1st option total cost: y = 240 + 8x
2nd option total cost: y = 600
b. Solve the system of equations. After how many members are the options equal?
y = 240 + 8x
y = 600
by solving we find
x = 45
y = 600
click here to see the step by step solution of the system of equations
the options are equal for 45 members.
c. When does the 1st option have the lower total cost?
240 + 8x < 600
x < (600-240)/8
x < 45
the 1st option have the lower total cost when the number of members is less than 45.
When does the 2nd option have the lower total cost?
240 + 8x > 600
x > (600-240)/8
x > 45
the 2nd option have the lower total cost when the number of members is more than 45.