Mindy, Jake and Donald shared a sum of money. The amount received by Jake was 2/3 the amount of money received by Donald. After Mindy had given $48 to Jake and $27 to Donald, Jake gave $3 to Donald. In the end, 3 of them had the same amount of money. Find the difference between the amount of money that Mindy and Jake had at first
First write down what they tell you.
j = 2/3 d
m-48-27 = j+48-3 = d+27+3
now just solve that for j,m,d and then you want m-j
Post your work if you get stuck.
First write down what they tell you.
j = 2/3 d
m-48-27 = j+48-3 = d+27+3
now just solve that for j,m,d and then you want m-j
=> m - 75 = j + 45 = d + 30
=> m - 75 = 2/3 d + 45 = d + 30
=> m - 75 = 2/3 d - d = 30 - 45
=> (2/3 - 1) d = 30 - 45
=> ((2-3)/3) d = - 15
=> d * 1/3 = - 15
=> d = - 15/1/3
=> d = - 15 * 3/1
=> d = - 45
=> m - 75 = d = - 45
=> m - 75 = - 45
=> m = - 45 + 75
= 30
J = 2/3 d
=> J = 2/3 * - 45
= - 30
M - J = 30 - 30
= 0
Answer
J = -30
m = 30
d = -45
m - j = 0
Jake = 2/3 of Donald
Mindy = 2 (Jared & Donald) 2 (x + 2/3x)
Mindy = 2 ((3x + 2x)/3) = $10x/3
Mindy gave $48 and $27 to Jake and Donald respectively so Mindy have 10x/3 - $48 - $27
Mindy = 10x/3 - $75
Jake = 2/3x + $48 - $3 = 2/3x + $45
10x/3 - $75 = 2/3x + $45
10x/3 - 2/3x = $45 + $75
8x/3 = $120
Answer $120
First write down what they tell you.
j = 2/3 d
m-48-27 = j+48-3 = d+27+3
now just solve that for j,m,d and then you want m-j
j = 2/3 d
m-48-27 = j+48-3 = d+27+3
j + 48 - 3 = d + 27 + 3
2/3 d + 48 - 3 = d + 27 + 3
45 - 30 = d - 2/3 d
15 * 3 = 3d - 2d
45 = d
j = 2 * 15 = 30
j = 30
m - 48 - 27 = 45 + 27 + 3
m - 75 = 75
m = 75 + 75
m = 150
m - j = 150 - 30 = 120
m - j = 120
To solve this problem, let's break it down step by step.
Step 1: Set up the equations
Let's denote the amount of money received by Mindy, Jake, and Donald as M, J, and D, respectively. We'll also denote the final amount of money they all have as F (which is the same for all three of them).
From the problem, we are given the following information:
- Jake received 2/3 of the amount received by Donald: J = (2/3)D
- After giving $48 to Jake, Mindy has (M - 48) left: M - 48 = F
- After giving $27 to Donald, Mindy has (M - 27) left: M - 27 = F
- After giving $3 to Donald, Jake has (J - 3) left: J - 3 = F
Step 2: Simplify the equations
Let's simplify the equations by substituting J with (2/3)D:
- J = (2/3)D
- M - 48 = F
- M - 27 = F
- (2/3)D - 3 = F
Step 3: Equate the final amounts
Since all three of them have the same final amount (F), we can set up the following equation:
M - 48 = M - 27 = (2/3)D - 3
Step 4: Solve for D
Let's solve the equation for D:
M - 48 = M - 27 [Since M - 48 = M - 27 = (2/3)D - 3]
-48 = -27 [Simplifying]
-21 = (2/3)D - 3 [Rearranging]
(2/3)D = -18 [Adding 3 to both sides]
D = -27 [Multiplying both sides by 3/2]
Step 5: Find the difference between the amounts of money of Mindy and Jake at first
To find the difference between Mindy's and Jake's initial amounts, we need to substitute the value of D into J:
J = (2/3)D = (2/3)(-27) = -18
The difference is the absolute value of the difference between Mindy's and Jake's initial amounts:
|J - M| = |-18 - M|
There you go! The difference between the amounts of money that Mindy and Jake had at first is |-18 - M|.