Question

The table shows the amount of money in your savings account over a period of $6$ weeks.

No. of Weeks	Account Balance
$0$	$\$100$
$1$	$\$155$
$2$	$\$210$
$3$	$\$265$
$4$	$\$320$
$5$	$\$375$
$6$	$\$430$

You plan to keep saving at the same rate until you have $\$825$ in the account. Which equation could you use to find the number of weeks, $n$, it would take to reach your goal?

• A. $55n=825$
• B. $100-n=825$
• C. $55n+100=825$
• D. $100n+55=825$

Answer 1

The correct option is C

$55n+100=825$

Explanation for the correct option:

No. of Weeks	Account Balance
$0$	$\$100$
$1$	$\$155$
$2$	$\$210$
$3$	$\$265$
$4$	$\$320$
$5$	$\$375$
$6$	$\$430$

Finding the rate of savings per week and constructing an $\mathrm{AP}$.

As $155-100=210-155=\cdots =430-375=55$, from the given table, we see that, in each week the savings amount is $\$55$.

Thus, the account balances in consecutive weeks form an $\mathrm{AP}$ with the first term $a=100$ and common difference $d=55$.

Suppose after $n$ number of weeks, the account balance will be $\$875$. So, the ${(n+1)}^{th}$ term of the $\mathrm{AP}$ will be $t_{n+1}=875$.

Finding the value of $n$

We know that for an AP with the first term $a$ and common difference $d$, the $n$th term will be $t_n=a+\left(n-1\right)d$.

Here, we shall use this equation to find the required number of weeks.

Here, $a=100,d=55,t_{n+1}=875$.

But by the above formula $t_{n+1}=a+nd$. Therefore, we must have:

$$\begin{gathered} a+nd=825 \\ \Rightarrow 100+n\times 55=825 \\ \Rightarrow 55n+100=825 \end{gathered}$$

Hence, option (C) is the correct answer.