40% of Peter’s salary is equal to 25% of Jason’s salary. If Jason’s salary is $684 more than Peter’s salary, how much money do they have altogether?
j = p+684
0.4p = 0.25j
0.4p = 0.25(p+684)
0.15p = 171
p = 1140
j+p = 1140 + 1140+684 = 2964
Peter's salary --- x
Jason's salary --- y
Let's just translate the English into Math.
"40% of Peter’s salary is equal to 25% of Jason’s salary"
----> (40/100)x = (25/100)y
40x = 25y
8x = 5y
y = (8/5)x
"Jason’s salary is $684 more than Peter’s salary"
tells me that if I subtract Peter's salary from Jason's, I will get 684
y - x = 684
substitute ....
(8/5) x - x = 684
(3/5)x = 684
x = 684(5/3) = 1140
since y = (8/5)x
y = (8/5)(1140) = 1824
the mystery is solved! Just state your conclusions.
To find out how much money Peter and Jason have altogether, we first need to find the value of Peter's salary.
Let's assume Peter's salary is represented by the variable 'P'.
We are given that 40% of Peter's salary is equal to 25% of Jason's salary. Mathematically, we can write this as:
0.4P = 0.25J
We also know that Jason's salary is $684 more than Peter's salary. This can be expressed as:
J = P + 684
Now, we can solve these two equations simultaneously to find the values of P and J.
1. Rearrange the first equation to get J in terms of P:
J = (0.4P) / 0.25
2. Substitute the value of J from the first equation into the second equation:
(0.4P) / 0.25 = P + 684
3. Simplify and solve for P:
0.4P = 0.25P + 684
0.4P - 0.25P = 684
0.15P = 684
P = 684 / 0.15
P ≈ $4,560
Now that we know Peter's salary, we can substitute this value into the second equation to find Jason's salary:
J = P + 684
J = 4,560 + 684
J ≈ $5,244
Finally, to find out how much money they have altogether, we add their individual salaries:
Total = Peter's salary + Jason's salary
Total = $4,560 + $5,244
Total ≈ $9,804
Therefore, Peter and Jason have a total of approximately $9,804 altogether.