Celia and ryan are starting a nutrition program. celia currently consumes 1200 calories a day and will increase that number by 100 calories each day. ryan currently consumes 3230 calories a day and will decrease that number by 190 each day. they will continue consuming that same number of calories per day. in how many days will that be?

C is Celia's calorie count and R is Ryan's. d = days
C = 1200 + 100d
R = 3230 - 190d
Since you want to find when they will consume the same amount of calories, you set the two equations equal to each other: 1200 + 100d = 3230 - 190d.
Then, subtract 1200 from both sides: 100d = 2030 - 190d. Next, add 190d to both sides: 290d = 2030. Therefore, the number of days is eqal to 2030/290, which is 7.