Question

100 POINTS PLEASE HURRY!!! Lamont’s grandmother started a stamp collection in 1932 (year 1) and added the same number of stamps to the collection each year. When Lamont’s mother received the collection at the end of 1972, there were 203 stamps in the collection. Lamont’s mother continued to add the same number of stamps to the collection each year. When Lamont received the collection at the end of 2009, there were 383 stamps in the collection. If Lamont continued to add the same number of stamps each year, how many stamps were in the collection at the end of 2018 (year 87)?
A. 403
B. 433
C. 563
D. 663

Answer 1

Answer:c.563

Step-by-step explanation:

Answer 2

433 stamps were in collection at the end of 2018.

What is a linear equation?

'A linear equation is an equation in which the highest power of the variable is always one. It is also known as a one-degree equation.'

According to the given problem,

We know,

y = mx + c,  where m = constant rate of change,

c = value of the y-intercept.

Let x = number of years after 1932.

y =  Number of stamps after x years.

In 1972 (year 40), there were 203 stamps in the collection.

⇒ 203 = 40m + c (1)  [rate of change in number of stamps  is constant]

In 2009 (year 77), there were 383 stamps in the collection.

⇒ 383 = 76m + c (2)

Now, for solving the equations, Subtracting (1) from (2)

⇒ 180 = 36m

⇒ m = 5

⇒ 5 stamps added per year.

Now for the value of c, putting the value of m in equation (1)

⇒ 203 = 40m + c

⇒ 203 = (40 × 5) + c

⇒ c = 203 - 200

⇒ c = 3

Stamps in 2018 (year 87)  = 87m + c  

                                          = (5 × 86) + 3

                                          = 430 + 3

                                          = 433

Hence, we can conclude that 433 stamps were in collection at the end of 2018.

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