Zarah keeps RM80 in her 'Giant Fund' at the end of the first month and continues saving every month, RM10 more than the previous month.(a) Just after Zarah's RM280 deposit, determine the number of weeks that she has saved the money.
How many times does she have to add 10 to 80 to make it to 280
80 + 20*10 = 280
Looks like 20 months to me
Tn= 280
280=80 ( n-1) (10)
200 = 10n - 10
210 = 10n
21 = n
To determine the number of weeks that Zarah has saved the money, we need to find out how many months it took for her to deposit RM280.
First, let's set up an equation to represent the problem.
Let x represent the number of months it took for Zarah to deposit RM280.
We know that Zarah starts with RM80 in her 'Giant Fund' account, and each subsequent month she saves RM10 more than the previous month. Therefore, the amount saved in the x-th month is given by:
Amount saved in the x-th month = RM80 + (x-1) * RM10
Since we want to find the number of months it took for Zarah to deposit RM280, we need to solve the following equation:
RM80 + (x-1) * RM10 = RM280
Now let's solve the equation:
RM80 + (x-1) * RM10 = RM280
(x-1) * RM10 = RM280 - RM80
(x-1) * RM10 = RM200
Dividing both sides of the equation by RM10:
(x-1) = RM200 / RM10
(x-1) = 20
Adding 1 to both sides of the equation:
x = 20 + 1
x = 21
Therefore, it took Zarah 21 months to deposit RM280.
Now, let's determine the number of weeks. Since there are 4 weeks in a month, we can multiply the number of months by 4 to get the number of weeks.
Number of weeks = 21 * 4 = 84
Therefore, Zarah saved the money in 84 weeks.
To determine the number of weeks Zarah has saved the money after her RM280 deposit, we will need to calculate the total amount she has saved prior to that deposit.
From the given information, we know that Zarah initially saved RM80 at the end of the first month. Every subsequent month, she saves RM10 more than the previous month.
We can create a sequence to represent Zarah's monthly savings:
Month 1: RM80
Month 2: RM80 + RM10 = RM90
Month 3: RM90 + RM10 = RM100
Month 4: RM100 + RM10 = RM110
Generalizing this pattern, we can observe that the total savings after n months can be calculated using the formula:
Total savings = RM80 + (RM10 * (n-1))
Now, to find the number of weeks Zarah has saved the money after her RM280 deposit, we need to calculate the value of n that satisfies the equation:
RM280 = RM80 + (RM10 * (n-1))
Rearranging the equation, we have:
RM10 * (n-1) = RM280 - RM80
RM10 * (n-1) = RM200
Now, we can solve for n by dividing both sides by RM10:
n - 1 = 20
n = 21
Therefore, Zarah has saved the money for 21 months. Since each month consists of approximately 4 weeks, we can estimate that she has saved the money for around 21 x 4 = 84 weeks.