Question

5. Lynn and her brother were born on the same date in different years. Lynn was 5 years old when her brother was 2. Use this information to complete the table. Lynn's age Her brother's age a) 15 b) 25 d) Is there a proportional relationship between Lynn's age and her brother's age? e) Explain your reasoning.

Answer 1

- Lynn's age is 5 years more than her brother's age in each case.

- There is a proportional relationship between Lynn's age and her brother's age because for every increase of 1 year in her brother's age, Lynn's age increases by 1 year as well.

Step-by-step explanation:

To complete the table, we can use the given information that Lynn was 5 years old when her brother was 2. We will calculate their ages based on this information.

Lynn's age | Her brother's age

-----------------------------------

a) 15 | 12

b) 25 | 22

c) |

d) |

e) |

To find Lynn's age, we can add 5 years to her brother's age in each case:

a) Lynn's age: 15, Her brother's age: 15 - 5 = 10

b) Lynn's age: 25, Her brother's age: 25 - 5 = 20

Now, let's analyze the given information and determine if there is a proportional relationship between Lynn's age and her brother's age.

In this case, Lynn's age is always 5 years more than her brother's age. This means that for every increase of 1 year in her brother's age, Lynn's age increases by 1 year as well. Therefore, there is a proportional relationship between Lynn's age and her brother's age.

To summarize:

- Lynn's age is 5 years more than her brother's age in each case.

- There is a proportional relationship between Lynn's age and her brother's age because for every increase of 1 year in her brother's age, Lynn's age increases by 1 year as well.

Answer 2

Lynn's age and her brother's age have a consistent difference of 3 years which indicates a linear but not proportional relationship. At any given age of Lynn, her brother's age can be found by subtracting 3 years.

Step-by-step explanation:

The question addresses the concept of a proportional relationship in Mathematics, specifically looking at how the ages of Lynn and her brother scale as they grow older. When Lynn was 5, her brother was 2, meaning there was a difference of 3 years between them. This gap will stay constant throughout their lives.

a) When Lynn is 15 years old, her brother will be 15 - 3 = 12 years old.

b) When Lynn is 25 years old, her brother will be 25 - 3 = 22 years old.

d) There is not a proportional relationship because their ages do not change at the same ratio; however, there is a linear relationship since the age difference is consistent.

e) The reasoning is that in a proportional relationship, for every increase in Lynn's age, her brother's age should increase by the same multiplicative factor, which is not the case here.