Stanley and Terence had a sum of money in the ratio 1:5. Terence 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?
Stanley : Trerence = 1 : 5 = x : 5x = 3x : 15x
Terence : vincent = 3 : 2 = 3x : 2x = 15x : 10x
(I wanted the ratio term for Terrence to be the same)
Stan: Ter:Vin = 3x : 15x : 10x
28x = 560
x = 20
So Stan had 60, Ter had 300 and Vin had 200
(notice all conditions are met correctly)
Finish it up
Let's solve this step-by-step.
Step 1: Let's assume that Stanley has an amount of money represented by x dollars.
Therefore, Terence would have 5x dollars. (since the ratio of Stanley and Terence is 1:5)
Step 2: Now let's determine the ratio between Terence and Vincent.
If Terence has 5x dollars, and the ratio of Terence to Vincent is 3:2, we can set up the following equation:
5x / (3/2) = 560
Step 3: Let's solve for the value of x.
To simplify the equation, multiply both sides by (3/2):
5x * (2/3) = 560 * (2/3)
10x/3 = 1120/3
10x = 1120
Step 4: Now solve for x by dividing both sides by 10:
x = 1120/10
x = 112
Step 5: Thus, Stanley has $112.
Step 6: To find the amount of money Vincent has, we will find the value of Terence first.
Since Terence has 5 times the amount of money that Stanley has, Terence has:
5 * $112 = $560
Step 7: Now let's calculate how much money Vincent has.
Since the total amount of money is $560, we can subtract the amount of money Terence has from the total to find how much money Vincent has:
$560 - $560 = $0
Step 8: Therefore, Vincent has $0.
Step 9: Finally, to find how much more money Vincent has than Stanley, we subtract Stanley's amount from Vincent's amount:
$0 - $112 = -$112
Step 10: Vincent has $112 less than Stanley.
Therefore, Vincent has $112 less than Stanley.