CPM Homework Help : A2C Problem 2-39

Lona received a stamp collection from her grandmother. The collection is in a leather book and currently has $120$ stamps. Lona joined a stamp club, which sends her $12$ new stamps each month. The stamp book holds a maximum of $500$ stamps.

Complete the table below.
Hint (a):
Continue adding $12$ to find months 2-5.
Table (a):
Answer (a):
How many stamps will Lona have after one year?
Hint (b):
See part (a). (Continue until month twelve.)
Write an equation to represent the total number of stamps that Lona has in her collection after n months. Let the total be represented by $t\left(n\right)$ .
Hint (c):
Remember that the initial amount was $120$ stamps and the rate is $12$ stamps per month.
Answer (c):
Use these values to make an equation.
$t\left(n\right) = 120 +12n$
Solve your equation for $n$ when $t\left(n\right) = 500$ . Will Lona be able to fill her book exactly with no stamps remaining? How do you know? When will the book be filled?

Month	Stamps
$0$	$120$
$1$	$132$
$2$
$3$
$4$
$5$

Step 1(d):

Substitute $500$ for $t\left(n\right)$ .

$500 = 120 + 12n$

Step 2(d):

Solve for $n$ .

$\textit{n}=31\frac{2}{3}$

Answer (d):

Lona will not be able to fill her book exactly, with no leftover stamps, because when the equation is solved for $n$ , the result is a mixed number. It will be filled in $32$ months.