Final answer:
To find the total amount, we divide Riya's share of $658 by her part of the ratio, 7, to find the value of one part ($94). Then we multiply the value of one part by the total parts (12) to get the total amount ($1128). The provided answer options do not include the correct calculation result.
Step-by-step explanation:
To find out the total amount of money divided between Riya and Raj when we know that Riya's share is $658 and the ratio of their money is 7:5, we first need to express Riya's share as part of the whole amount represented by the ratio. The ratio gives us two parts, 7 parts for Riya and 5 parts for Raj. We therefore divide Riya's share by the number of parts allocated to her to find the value of one part:
Riya's share / Riya's ratio = One part
$658 / 7 = $94 (The value of one part)
Now that we have the value of one part, we can find the total number of parts by adding the parts of the ratio (7 + 5 = 12 parts). Then we multiply the value of one part by the total number of parts to find the whole amount:
Total amount = Value of one part × Total number of parts
Total amount = $94 × 12 = $1128
However, this total is not listed in the answer options, which means there must be an error in our calculation or the provided answer choices are not correct. Given the calculation above, the closest correct answer is not provided among the options A) $986, B) $822, C) $1022, or D) $876. Please double-check the information and calculation for accuracy.