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?
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).
initial amounts: 12x and 13x
then we are told that 12x = 3(13x-63)
Now. Find x, and then you can answer the questions.