Melissa has 1/2 as much money as Paul. Tom has 3/5 as much money as Melissa. If Paul has $42 more than Tom, how much do the three children have altogether?
A little trick avoiding fractions ....
let Melissa's amount be 5x
then Tom has 3x
Paul has 10x
10x - 3x = 42
solve for x, and sub back into my definitions.
Thx!
To solve this problem, let's start by assigning variables to the unknown quantities.
Let's assume that Paul has x dollars.
Since Melissa has 1/2 as much money as Paul, Melissa has (1/2)x dollars.
Since Tom has 3/5 as much money as Melissa, Tom has (3/5) * (1/2)x = (3/10)x dollars.
We know that Paul has $42 more than Tom, so we can write the equation: x = (3/10)x + $42.
To solve this equation, let's isolate the x term:
x - (3/10)x = $42
(7/10)x = $42
Now, we can solve for x:
x = ($42) / (7/10)
x = $420 / 7
x = $60
So, Paul has $60, Melissa has 1/2 * $60 = $30, and Tom has 3/10 * $60 = $18.
To calculate the total amount of money the three children have altogether, we add their individual amounts of money:
Total = $60 + $30 + $18
Total = $108
Therefore, the three children have a total of $108 altogether.