Question

Julia loves collecting baskets. Every month she adds two new baskets to her collection. In the month of March she has 60 baskets. She’s worried she will soon run out of room in her apartment to keep her baskets. Write an equation that represents the percent of change of her basket collection from the beginning of the year to the end of the year, then solve.

Answer 1

Step-by-step explanation: The linear function that represents the number of baskets in the month of the year is given as follows:

The percentage of her collection that she needs to get rid of is of 3.85%.

The definition of a linear function is:

y = b + mx

In which the parameters of the equation are given as follows:

•b is the value of y when x=0

•m is the rate of change for each unit of x

Every month she adds 2 new baskets to her collection, hence the slope is: m = 2

Then: y = b + 2x

From the March amount, when x = 3, y = 60, hence the intercept b is given as follows:

60 = b + 6

b = 54

Hence the equation is: y = 54 + 2x

At the end of the year (12 months) the number of baskets that she will have is:

y = 54 + 2 × 12 = 78

Hence, she has to get rid of 3 baskets, as 78 - 75 = 3, and the percentage is of:

p = 3/78 × 100% = 3.85%.

Answer 2

The linear function that represents the amount of baskets in the xth month of the year is given as follows:

The percentage of her collection that she needs to get rid of is of 3.85%.

Linear Function:-

The definition of a linear function is:

y = b + mx

In which the parameters of the equation are given as follows:

•b is the value of y when x=0

•m is the rate of change for each unit of x

Every month she adds 2 new baskets to her collection, hence the slope is of : m = 2

Then: y = b + 2x

From the March amount, when x = 3, y = 60, hence the intercept b is given as follows:

60 = b + 6

b = 54

Hence the equation is: y = 54 + 2x

At the end of the year (12 months) the amount of baskets that she will have is of:

y = 54 + 2 × 12 = 78

Hence, she has to get rid of 3 baskets, as 78 - 75 = 3, and the percentage is of:

p = 3/78 × 100% = 3.85%.