Final answer:
To find the ratios of Kieran's savings, Simon's savings, and their total savings, we start with an equation that relates Kieran's savings to Simon's savings. We then calculate the ratios using this equation. Kieran's savings is 9/13 times the total amount of money saved, while Simon's savings is 1/13 times the total amount of money saved. Finally, we find that the total amount of money saved by both of them is 2K - 28 dollars.
Step-by-step explanation:
To answer the questions, let's assume that Simon's savings is represented by 'S' and Kieran's savings is represented by 'K'. Given that Kieran's savings is 9/2 of Simon's savings, we can write this as an equation: K = (9/2)S.
(a) The ratio of Kieran's savings to Simon's savings to their total savings can be calculated by adding their savings together: K + S = (9/2)S + S = (11/2)S. So, the ratio is K: S: Total savings = (9/2)S: S: (11/2)S.
(b) To find how many times Kieran's savings is the total amount of money saved, we divide K by the total savings: K / (K + S) = (9/2)S / ((9/2)S + S) = (9/2)S / ((9/2)S + 2S) = (9/2)S / ((9/2 + 4/2)S) = (9/2)S / ((13/2)S) = 9/13. So, Kieran's savings is 9/13 times the total amount of money saved.
(c) Similarly, to find how many times Simon's savings is the total amount of money saved, we divide S by the total savings: S / (K + S) = S / ((9/2)S + S) = S / ((9/2)S + 2S) = S / ((9/2 + 4/2)S) = S / ((13/2)S) = 1/13. So, Simon's savings is 1/13 times the total amount of money saved.
(d) It is given that Simon saves $28 less than Kieran, so we can write this as an equation: S = K - 28. To find their total savings, we add their savings together: Total savings = K + S = K + (K - 28) = 2K - 28. Therefore, both of them save altogether 2K - 28 dollars.