Answer
The answer is: $\$825$ to John, $\$1650$ to Maria and $\$2475$ 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 that $x + y + z = 4950$, because the addition of money given to each one has to equal the total amount of money.
$x+y+z=4950$ ->Eq. 1
From " Maria receives twice as much as John", we get:
$y=2x$ ->Eq. 2
From "Betsy receives three times as much as John", we get:
$z=3x$ ->Eq. 3
Step 2:
Solve the system of equations. Using the substitution method,
-> Substitute Eq. 2 and Eq. 3 into Eq. 1
$x+2x+3x=4950$
$6x=4950$
$x=\frac{4950}{9}$
$x=825$
-> Substitute the value for x in Eq. 2
$y=2(825)$
$y=1650$
-> Substitute the value for x in Eq. 3
$z=3(825)$
$z=2475$
Step 3:
The answer is $\$825$ to John, $\$1650$ to Maria and $\$2475$ to Betsy.
