Final answer:
Jane has $25, Rafael has $19, and Ali has $76 in their wallets. We found these amounts by setting up equations based on the given information and solving for each person's amount.
Step-by-step explanation:
To solve the problem of how much money Jane, Ali, and Rafael have in their wallets, let's define variables for the amount of money each person has. Let J represent Jane's amount, A represent Ali's amount, and R represent Rafael's amount. According to the problem, we know the following:
- Rafael has $6 less than Jane: R = J - 6
- Ali has 4 times what Rafael has: A = 4R
- The total amount they have is $120: J + A + R = 120
Now, let's use these equations to find the amounts for Jane, Ali, and Rafael. We'll substitute the expressions for R and A into the third equation:
J + (4R) + (J - 6) = 120
Combining like terms and solving for J gives us:
2J + 4R - 6 = 120
However, we can express R in terms of J to get J only on one side:
2J + 4(J - 6) - 6 = 120
Expanding this we get:
2J + 4J - 24 - 6 = 120
6J - 30 = 120
Adding 30 to both sides gives us 6J = 150
Dividing both sides by 6 gives us J = 25
Knowing J, we can find R and then A:
R = J - 6 = 25 - 6 = 19
A = 4R = 4 * 19 = 76
Jane has $25, Rafael has $19, and Ali has $76 in their wallets.