Standard Form Division and Simple Interest Calculation
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1. (a) Evaluate, without using mathematical tables or calculator, $(3.69 \times 10^{5}) \div (1.64 \times 10^{-3})$, leaving your answer in the Standard form.
(b) A man invested ₦20,000 in bank A and ₦25,000 in bank B at the beginning of a year. Bank A pays simple interest at a rate of $y\%$ per annum and B pays $1.5 y\%$ per annum. If his total interest at the end of the year from the two banks was ₦4,600, find the value of $y$.
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Step by Step Written Solution
In this exercise, we have two parts. Part a asks us to divide numbers in standard form, and part b is a simple interest problem. Let's start with part a.
Part (a): Division in Standard Form
We need to evaluate three point six nine times ten to the fifth power, divided by one point six four times ten to the negative third power. We'll express this as a fraction first.
We can separate the decimal coefficients and the powers of ten to make calculation easier.
Let's focus on the decimal part. If we multiply both the numerator and denominator by one hundred, it becomes three hundred and sixty-nine divided by one hundred and sixty-four.
Notice that both numbers are divisible by forty-one. Three sixty-nine divided by forty-one is nine, and one sixty-four divided by forty-one is four. Nine fourths is two point two five.
Now for the powers of ten. Using the laws of indices, when we divide, we subtract the exponents. Five minus negative three becomes five plus three, which is eight.
Combining these two results, we get our final answer in standard form.
Now let's move on to part b, which involves simple interest calculation from two different bank investments.
Part (b): Simple Interest Problem
| Investment | Principal (P) | Rate (R) | Time (T) |
|---|---|---|---|
| Bank A | \text{N}20,000 | y\% | 1 \text{ year} |
| Bank B | \text{N}25,000 | 1.5y\% | 1 \text{ year} |
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