Stanley and Terrence had a sun of money in the ratio 1:5. Terrence and Vincent had a sum of money in the ratio 3:2. They had a total of $560 altogether. How much more money did Vincent have than Stanley?
1:5 = 3:15
3:2 = 15:10
s:t:v = 3:15:10
28x = 560
x = 20
so
s:t:v = 60:300:200
v-s = 200-60 = 140
Thanks
To solve this problem, we need to determine the amounts of money each person had. Let's break it down step by step.
Let's assume that Stanley had x dollars. Since the ratio of Stanley's money to Terrence's money is 1:5, Terrence must have 5x dollars.
Similarly, let's assume that Terrence had y dollars. Since the ratio of Terrence's money to Vincent's money is 3:2, Vincent must have (2/3)y dollars.
We are given that the total amount of money they had altogether is $560. Thus, the sum of their individual amounts of money is x + y + (2/3)y = 560.
To solve for the variables x and y, we can simplify the equation:
(5/3)y + x = 560.
Now we can solve for y:
(5/3)y = 560 - x,
y = (3/5)(560 - x).
Since Terrence had y dollars, we can substitute y with (3/5)(560 - x) in the ratio equation for Terrence and Vincent:
(3/5)(560 - x) / (2/3) = (3/2)(560 - x).
Let's solve the equation for x:
(3/5)(560 - x) / (2/3) = (3/2)(560 - x),
9(560 - x) = 10(560 - x),
5040 - 9x = 5600 - 10x,
x = 560.
So, Stanley had $560.
Now, let's find out how much money Vincent had. We can substitute the value of x into the expression for Vincent's money:
Vincent = (2/3)y = (2/3)(560 - x) = (2/3)(560 - 560) = (2/3)(0) = $0.
Therefore, Vincent had $0, and Stanley had $560. Thus, Vincent had $560 - $0 = $560 more than Stanley.