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Answer :
After Rob has lost, he will have 120 dollars. We can work this out by
establishing that if Rob had 280 dollars before the final competition,
and the ration at the point was 4 to 7, then this means that Tom must
have had 4/7 of what Rob had, so x=4/7 * 280, x = 4 x 40, x = 160. This
means that Tom had 160 dollars and Rob had 280. Adding this together
they have a combined 440 dollars, but the ratio is now 8:3. There are 11
parts to the ration, due to the fact that 8 and 3 is 11, so we need to
work out one part of the ratio - 440 divided by 11 equals forty. This
means that Tom has 8 multiplied by 40 (320 dollars) and Rob has 40
multiplied by 3, so 120 dollars.
establishing that if Rob had 280 dollars before the final competition,
and the ration at the point was 4 to 7, then this means that Tom must
have had 4/7 of what Rob had, so x=4/7 * 280, x = 4 x 40, x = 160. This
means that Tom had 160 dollars and Rob had 280. Adding this together
they have a combined 440 dollars, but the ratio is now 8:3. There are 11
parts to the ration, due to the fact that 8 and 3 is 11, so we need to
work out one part of the ratio - 440 divided by 11 equals forty. This
means that Tom has 8 multiplied by 40 (320 dollars) and Rob has 40
multiplied by 3, so 120 dollars.
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Final answer:
By using ratios and the given information about Rob's initial amount, we can calculate that Rob now has $120 after losing the bet.
Explanation:
The question involves a problem where the ratios of money held by Tom and Rob change due to a bet. Initially, the ratio of Tom's to Rob's money was 4:7. After Rob lost, his ratio to Tom's money became 8:3. Since it is given that Rob had $280 before the last competition, we need to find out how much Rob has now after losing the bet.
To solve this problem, we start by converting the initial ratio of Tom's to Rob's money into monetary values. Since Rob had 7 parts of the total money and his share was $280, we find the value of one part by dividing $280 by 7, which is $40. This means that initially, Tom had 4 parts, so he had,
4 * $40 = $160.
After the competition, Tom's money in relation to Rob's money is in the ratio of 8:3. But we can observe that this ratio must represent the same total amount of money as before since only their distribution has changed. Thus, we know that 8 parts for Tom and 3 parts for Rob must equal $440 (the total they had together initially). Therefore, one part is now worth.
$440 / (8 + 3)
= $440 / 11
= $40.
So, Rob, having 3 parts in this new ratio, now has 3 * $40 = $120.
