The ratio of the amount of money Jason had to the amount of money Wilson had was 12 to 13 after Wilson spent $63 Jason had three times as much money as Wilson a)how much money did Jason have? b) How much money did they have all together in the end?
initial amounts: 12x and 13x
then we are told that 12x = 3(13x-63)
Now. Find x, and then you can answer the questions.
To solve this problem, we need to break it down step by step.
Let's assign variables to the unknowns:
- Let J represent the amount of money Jason had initially.
- Let W represent the amount of money Wilson had initially.
Based on the information given, the ratio of Jason's to Wilson's money was 12:13. This can be expressed as (J/W) = 12/13.
After Wilson spent $63, Jason then had three times as much money as Wilson. We can now set up two equations based on the given information:
1. J = 3(W - 63) -- Jason had three times as much money as Wilson after the expenditure.
2. (J/W) = 12/13
Now, let's solve for the unknowns:
Solving Equation 1:
J = 3(W - 63)
J = 3W - 189 -- Distribute the 3
Substituting J = 3W - 189 into Equation 2:
(J/W) = 12/13
(3W - 189)/W = 12/13 -- Substitute J with 3W - 189
Cross-multiplying:
13(3W - 189) = 12W
39W - 2463 = 12W -- Distribute the 13
Simplifying:
39W - 12W = 2463
27W = 2463
W = 91 -- Divide both sides by 27 to solve for W.
Now that we have found W, we can substitute it back into Equation 1 to find J:
J = 3(W - 63)
J = 3(91 - 63)
J = 3(28)
J = 84
Therefore, Jason initially had $84 (answer to part a).
To find the answer to part b, we need to add the amount of money they had after Wilson's expenditure:
Total money = J + W - 63
Total money = 84 + 91 - 63
Total money = 112
hence, they had a total of $112 in the end (answer to part b).