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61 The library in. Natchitoches had about 60,000 volumes in March 2004 and was adding about 400 volumes per month.
A Write an equation expressing
y, the total number of volumes in the library, in terms of
x, the number of months after March 2004.

y=60,000+400 x
B About how many volumes will the library have in September 2005?
C About when will the library have 80,000 volumes?

$61$ The library in. Natchitoches had about $60$ , $000$ volumes in March $2004$ and was adding about $400$ volumes per month. $\newline$ A Write an equation expressing $y$ , the total number of volumes in the library, in terms of $x$ , the number of months after March $2004$ . $\newline$ $y=60,000+400 x$ $\newline$ B About how many volumes will the library have in September $2005$ ? $\newline$ C About when will the library have $80$ , $000$ volumes?

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Write a linear function: word problems

Full solution

Q.

61

The library in. Natchitoches had about

60

,

000

volumes in March

2004

and was adding about

400

volumes per month.

\newline

A Write an equation expressing

y

, the total number of volumes in the library, in terms of

x

, the number of months after March

2004

.

\newline

y=60,000+400 x

\newline

B About how many volumes will the library have in September

2005

?

\newline

C About when will the library have

80

,

000

volumes?

Write Equation: Write an equation for the total number of volumes in the library after $x$ months. $\newline$ The library starts with $60,000$ volumes and adds $400$ volumes each month. The relationship between the total number of volumes, $y$ , and the number of months after March $2004$ , $x$ , is linear. $\newline$ $y =$ initial volumes $+$ (volumes added per month $*$ number of months) $\newline$ $y = 60,000 + 400x$
Calculate Months: Calculate the number of months between March $2004$ and September $2005$ . $\newline$ March $2004$ to March $2005$ is $12$ months, and from March $2005$ to September $2005$ is an additional $6$ months. So, the total number of months is $12 + 6 = 18$ months.
Substitute Months: Substitute the number of months into the equation to find the total number of volumes in September $2005$ . $\newline$ Using the equation from Step $1$ : $\newline$ $y = 60,000 + 400x$ $\newline$ $y = 60,000 + 400(18)$ $\newline$ $y = 60,000 + 7,200$ $\newline$ $y = 67,200$
Determine Volumes: Determine when the library will have $80,000$ volumes. $\newline$ We need to solve for $x$ when $y$ is $80,000$ using the equation from Step $1$ . $\newline$ $80,000 = 60,000 + 400x$ $\newline$ $20,000 = 400x$ $\newline$ $x = \frac{20,000}{400}$ $\newline$ $x = 50$
Convert to Date: Convert the number of months into a date. $\newline$ Since $x$ is the number of months after March $2004$ , and $x$ is $50$ , we add $50$ months to March $2004$ . $\newline$ March $2004$ + $50$ months = March $2008$ + $2$ months = May $2008$ . $\newline$ The library will have $80,000$ volumes in May $2008$ .

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