# Tutor profile: Jennifer C.

## Questions

### Subject: Pre-Algebra

I am a number that when multiplied by 4, I am 640. What number am I?

In order to find what number I am, I have to undo the multiplication operation. The opposite or inverse of multiplication is division. Therefore, you have to take 640 and divide by 4. 640 divided by 4 is 160. I am the number 160.

### Subject: Basic Math

Laura and Stephanie are buying dog food for their dog, Abbie. Abbie eats 1/2 cup of dog food per day. If the bag of dog food has 12 cups of food, how many days will the bag of dog food last Abbie?

One way to determine how many days Abbie can eat the dog food would be to create a chart. For the first day, Abbie eats 1/2. The second day Abbie would eat 1 cup total, 1/2 from the first day and 1/2 from the second day. The third day Abbie would eat 1 1/2 cups total. The fourth day she eats 2 cups total of the bag of dog food. If you keep going, you find that in 24 days, Abbie will eat a total of 12 cups, which is the entire bag of dog food. Therefore, the bag of dog food will last 24 days.

### Subject: Algebra

John is looking to change his cell phone company. Company A charges an initial fee of $5 per month plus an additional 30 cents per minute talked during the month. Company B charges a flat fee of $20.50 per month for unlimited calls. How long would John need to talk each month for Company B to be the best choice?

When looking at the two cell phone companies, John needs to come up with a way to decide which way is best. He could create equations for each company and find when the solutions will be the same. He could create tables and calculate times when the solutions will be the same. For this case, I would look at two equations. Company A would be modeled as y = 0.30x + 5, where .30 represents the cents per minute and the 5 represents the initial fee each month. Company B would be modeled as y = 20.50. This particular equation does not have an x in it because the cost never changes each month. When you look at these equations together, you can find where they are the same by setting them equal. 0.30x + 5 = 20.50 is the new equation by replacing/substituting the value from the second y into the first y. Then solve by subtracting 5 from the left to the right side. This creates a zero pair where the 5 is no longer on the left side. Then you are left with 0.30x = 15.50. Now, to find the value of x, divide by 0.30. This is because you would originally be multiplying that value by the minutes. 15.50 divided by 0.30 is 51.66667. This means that when John talks for 51.66667 minutes, the two plans will cost the same. In order for John to save month each month with Company B, he would need to talk for more than 51.6667 minutes. Therefore, John would need to talk for at least 52 minutes each month for Company B to be the best choice.

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