Question

Formulate a linear model to represent the situation of Abigail collecting rare dolls, starting at age 5 with 12 dolls and receiving two more dolls each year starting from her 6th birthday. Determine how many dolls she will have by the age of 15 and at what age she will have a total of 40 dolls.

Answer 1

A linear model that describes the number of dolls Abigail collects over the years is D = 2(A - 5) + 12. Abigail will have 32 dolls at age 15. She will be 19 years old when her collection reaches 40 dolls.

Step-by-step explanation:

To create a linear model representing Abigail's collection of rare dolls, we start with the given information that she has 12 dolls at age 5 and receives an additional 2 dolls every year after her 6th birthday. The linear model can be expressed as D = 2(A - 5) + 12, where D represents the number of dolls, and A is Abigail's age. To find out how many dolls Abigail will have by the age of 15, we substitute A with 15 in the equation: D = 2(15 - 5) + 12 = 2(10) + 12 = 20 + 12 = 32. Therefore, Abigail will have 32 dolls by the age of 15.

Now, to determine at what age Abigail will have a total of 40 dolls, we solve the equation for A. This gives us 40 = 2(A - 5) + 12. Simplifying, we get: 40 - 12 = 2(A - 5), 28 = 2A - 10, 38 = 2A, and therefore A = 38 / 2 = 19. Abigail will be 19 years old when she has 40 dolls.