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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 this pattern until they are both consuming the same number of calories per day. In how many days will that be? SHOW YOUR WORK

Answer :

ajmal11
Let the number of days they take to consume same amount be d.

Celia's equation for consumption is :

Y = 1200 + 100d
Ryan's consumption equation is :

Y = 3230 - 190d
We are looking for a time when these two will be equal.

We therefore equate the two equations as follows :

3230 - 190d = 1200 + 100d
We want to get the value of d.

3230 - 1200 = 100d + 190d

2030 = 290d

d = 2030/290

d = 7

The answer is thus :

7 days.

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