Tom and Ali had money in the ratio 6:11. The ratio of Tom’s expenditure to that of Ali is 4:3. If Tom spent 1/3 of his money and Ali had $475 left, how much did each of them have at first?
Totally WRONG
That set of answers is not even in the ratio of 6:11
tom : ali = 6:11 = 6x : 11x
expenses:
tom : ali = 4:3 = 4y : 3y
Ali has left: 6x - 4y
4y = (1/3)6x)
4y = 2x
x = 2y
For ali:
11x - 3y = 475
22x - 3y = 475
y = 25 , then x = 50
so tom had 6x or $300
ali had 11x or $550
check: tom:ali = 300:550 = 6:11 , check!!
ali has 475 left. Is 550 - 3(25) = 475, Check!!!
my answer is correct
Let's start by finding the total ratio of money that Tom and Ali had.
The given ratio of money held by Tom and Ali is 6:11.
To find the total ratio, we add the values in the ratio: 6 + 11 = 17.
Now, let's calculate the fraction of money Tom spent:
Tom spent 1/3 of his money, which means he had 2/3 of his money left.
We know that the fraction of money Ali had left is 475/total money, and Tom and Ali's total ratio is 17.
Therefore, Tom's fraction of money is (2/3) / 17.
Now, let's express the ratio of Tom's expenditure to Ali's expenditure in terms of their original money. The given ratio is 4:3.
Since the ratio of money held by Tom and Ali is 6:11, this means the ratio of their expenditure is also in the same proportion, 6:11. So, the ratio of Ali's expenditure to Tom's expenditure is 11:6.
Given that the ratio of expenditure is 4:3, we can set up the following equation:
11x / 6x = 4 / 3
Cross-multiplying gives us:
11x * 3 = 6x * 4
33x = 24x
So, x = 0.
However, if x = 0, it would mean that both Tom and Ali had no money to begin with, which is not possible.
Therefore, there seems to be an error or inconsistency in the information provided. Please double-check the given data and resubmit the question.
To solve this problem, let's break it down step by step:
Step 1: Set up the equations for the given information.
Let's assume that Tom had some amount of money - we'll call it "x" dollars.
Since the ratio of their money is 6:11, Ali's amount of money can be represented as 11x/6 dollars.
Step 2: Calculate Tom's expenditure.
According to the given information, Tom spent 1/3 of his money. So, his expenditure can be calculated as (1/3)x dollars.
Step 3: Calculate Ali's expenditure.
Since the ratio of Tom's expenditure to Ali's expenditure is 4:3, we can set up the equation:
(1/3)x / (Ali's expenditure) = 4/3
Cross-multiplying, we get:
(1/3)x = (4/3)*(Ali's expenditure)
Simplifying, we have:
(Ali's expenditure) = (1/4)*(1/3)x = (1/12)x dollars.
Step 4: Calculate the remaining money Ali had.
We are given that Ali had $475 left. So, we can say:
11x/6 - (1/12)x = $475
Multiplying through by 12 to get rid of the fraction, we have:
22x - x = 12*475
Simplifying, we get:
21x = 5700
Divide both sides by 21:
x = 270.
Step 5: Calculate the initial amount of money.
Now that we have the value of "x" (Tom's initial money), we can calculate the initial amounts for both Tom and Ali:
Tom's initial amount = x dollars = $270.
Ali's initial amount = 11x/6 dollars = 11/6 * 270 = $495.
Therefore, Tom initially had $270, and Ali initially had $495.