SOLUTION: g = -5t + 99 The variable t represents the number of tables Kathleen has set, and the variable g represents the number of glasses remaining. How many tables does Kathleen need t

Question 996029: g = -5t + 99
The variable t represents the number of tables Kathleen has set, and the variable g represents the number of glasses remaining. How many tables does Kathleen need to set in order to have just 74 glasses left to distribute?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
looks like there are 5 glasses per table.

g = -5t + 99

t is number of tables and g is number of glasses left

replace g with 74 and you get:

74 = -5t + 99
add 5t to both sides of this equation and subtract 74 from both sides of this eqution to get:
5t = 99-74
divide both sides of this equation to get:
t = (99-74)/5

solve for t to get t = (99-74)/5 = 25/5 = 5.

she starts with 99 glasses.
5 tables at 5 glasses apiece equals 25 glasses.
99 - 25 = 74.

in the equation of g = -5t + 99:

99 is the number of glasses she has when the number of tables is equal to 0.
this is because g = -5t + 99 becomes g = -5*0 + 99 which becomes g = 99.

the slope of this equation is -5.
this means that for every table that's added, the number of glasses remaining goes down by 5.
this can only occur if she places 5 glasses on each table.

when t = 5, the formula becomes:

g = -5*5 + 99 which then becomes g = -25 + 99 which then becomes g = 74.

5 tables were set and each table took 5 glasses, o the glasses remaining was 99 - 25 = 74.

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