When Todd won the one million dollar lottery, he kept some of the money(M) in a short term account at 4.2% and invested the remainder at 7.25%.
Write a relationship between I and A.
First tell us what I and A are supposed to mean.
I is Interest, but it doesn't list the definition of A.
To write a relationship between the interest earned (I) and the amount invested (A), we need to consider the interest rates and the proportions of money kept in different accounts.
Let's say Todd won a total of one million dollars, and he kept a portion of the money (M) in a short term account at a 4.2% interest rate. This means that the remaining amount, which is (1 - M), was invested at a 7.25% interest rate.
The interest earned on the money kept in the short term account can be calculated using the formula: I_short = M * 4.2% = 0.042M.
Similarly, the interest earned on the money invested can be calculated using the formula: I_invested = (1 - M) * 7.25% = 0.0725(1 - M).
The total interest earned, I, is the sum of the interest earned from the short term account and the interest earned from the investment:
I = I_short + I_invested
I = 0.042M + 0.0725(1 - M)
So, the relationship between I (interest earned) and A (amount invested) can be expressed as:
I = 0.042M + 0.0725(1 - M)
Note: The relationship assumes that the interest is earned over a certain period and uses simple interest calculations.