Question

Silvia has $1500 in her bank account.She spends $150 each week. A.) Write an equation that represents the relationship between the amount in Silvia’s bank account and the number of weeks.B.) What is the slope and what does it mean in the context of the problem?C.) What is the y-intercept and what does it mean in the context of the problem?D.) After how many week's will Silvia's account have a zero balance?

Answer 1

Given that Silvia has $1500 in her bank account, and she spends $150 each week, let x represent the number of weeks which she spend the entire amount in her bank account.

A) Equation that represents the relationship between the amount in Silvia’s bank account and the number of weeks:

Since it takes x weeks to spend the entire amount in her account, and where $150 is spent each week, we have

`\begin{gathered} \\ y=1500-150x \end{gathered}`

B) Slope and what it means in the context of the problem:

Using the equation of a line expressed as

`\begin{gathered} y=mx+c \\ where \\ m\Rightarrow slope\text{ of the line} \\ c\Rightarrow y-intercept\text{ of the line} \end{gathered}`

Comparing the line equation with the relationship in (A), we have

`slope\text{ = -150}`

Meaning in the context of the problem: The slope implies that for every week the amount in her bank account is reduced by $150.

C) y-intercept and what it mean in the context of the problem:

Comparing the relationship in A with the line equation in B, we have

`c=1500`

Meaning in the context of the problem: The y-intercept implies the initial amount in her bank account. (The value of y when x equals zero).

D) Number of weeks Silvia's account have a zero balance:

From (A), we equate y to zero to evaluate x

`\begin{gathered} y=1500-150x \\ when\text{ y=0,} \\ 0=1500-150x \\ subtract\text{ 1500 from both sides of the equation} \\ 0-1500=1500-150x-1500 \\ \Rightarrow-1500=-150x \\ divide\text{ both sides by the coefficient of x, which is -150} \\ (-1500)/(-150)=(-150x)/(-150) \\ \Rightarrow x=10 \end{gathered}`

Hence, Silvia's account will have a zero account in 10 weeks.