# A Puzzle of Changing Diets: Simba and Cuddles

## The Caloric Journey of Simba and Cuddles

A veterinarian is changing the diets of two animals, Simba and Cuddles. Simba currently consumes 1,150 Calories per day. That number will increase by 150 Calories each day. Cuddles currently consumes 2,750 Calories a day. That number will decrease by 170 Calories each day. The patterns will continue until both animals are consuming the same number of Calories each day.

## Question:

In how many days will that be? How many Calories will the animals be consuming each day then?

In __________ days Simba and Cuddles will be consuming the same amount of calories. Simba and Cuddles will be consuming __________ calories each day.### Final answer:

In 5 days, Simba and Cuddles will be consuming the same amount of calories. They will each be consuming 1,900 calories per day after both their daily caloric intakes change according to the given conditions.

### Explanation:

To determine when Simba and Cuddles will be consuming the same amount of calories per day, we need to set up an equation to find the point at which their dietary caloric intake intersects. Let's define *d* as the number of days after which they will have the same caloric intake.

Starting with Simba's intake, we know he starts at 1,150 Calories and increases by 150 Calories each day. So, Simba's caloric intake can be represented by the equation 1,150 + 150*d*. Cuddles starts at 2,750 Calories, decreasing by 170 Calories each day, which can be represented by 2,750 - 170*d*.

To find when they consume the same Calories, we set the equations equal to each other:

1,150 + 150*d* = 2,750 - 170*d*.

Now, we solve for *d*:

320*d* = 1,600

*d* = 1,600 / 320

*d* = 5

So, in 5 days, Simba and Cuddles will both consume the same amount of calories. To find out how many Calories that is:

1,150 + (150 × 5) = 1,150 + 750 = 1,900 Calories

Therefore, in 5 days Simba and Cuddles will be consuming the same amount of calories. Simba and Cuddles will be consuming 1,900 calories each day.

### Final answer:

In 8 days, Simba and Cuddles will be consuming the same amount of calories. They will each be consuming 2350 calories per day.

### Explanation:

To find out in how many days Simba and Cuddles will be consuming the same amount of calories, we need to set up an equation.

Let x represent the number of days it takes for Simba and Cuddles to consume the same number of calories. Simba's daily calorie consumption is given by the equation: 1150 + 150x. Cuddles' daily calorie consumption is given by the equation: 2750 - 170x.

Setting the two equations equal to each other, we have: 1150 + 150x = 2750 - 170x. Solving for x, we get x = 8.

So, in 8 days, Simba and Cuddles will be consuming the same amount of calories. They will each be consuming 2350 calories per day.