Answer
The answer is: $\$550$ to John, $\$1100$ to Maria and $\$3300$ to Betsy.
Work Step by Step
We assign the variables:
x = John's money
y = Maria's money
z = Betsy's money
Step 1:
Find the equations that represent the problem.
We know $x+y+z=4950$, because the addition of the money given to each one has to equal the total amount of money.
$x+y+z=4950$ -> Eq. 1
We can get the second equation from the wording in the problem.
From "Maria receives twice as much as John", we get:
$y=2x$ -> Eq. 2
We can get the third equation from the wording in the problem.
From "Betsy receives three times as much as Maria", we get:
$z=3y$ -> Eq. 3
Step 2:
Solve the system of equations. Using the substitution method,
-> Substitute eq. 2 into eq. 3
$z=3(2x)$ -> to find z in terms of x
$z=6x$ -> Eq. 4
-> Substitute eq. 2 and eq. 4 into eq. 1
$x+2x+6x=4950$
$9x=4950$
$x=\frac{4950}{9}$
$x=550$
-> Substitute the value for x in eq. 2
$y=2(550)$
$y=1100$
-> Substitute the value for y in eq. 3
$z=3(1100)$
$z=3300$
Step 3:
The answer is: $\$550$ to John, $\$1100$ to Maria and $\$3300$ to Betsy.
