Lia, Phil, and Cam collect a total of $200.30 for a holiday fundraiser. Phil collects $12.80 more than Lia. Cam collects 3 times as much as Lia. How much does each person collect?
P = L + 12.80
C = 3 L
so
L + 3 L + L + 12.80 = 200.30
5 L = 200.30 - 12.80
???
I'm in 5th grade, and this problem came up...
We haven't even learned basic algebra
To solve this problem, we can set up a system of equations.
Let's represent the amount that Lia collects as "x".
Since Phil collects $12.80 more than Lia, we can represent the amount Phil collects as "x + $12.80".
And since Cam collects 3 times as much as Lia, we can represent the amount Cam collects as "3x".
We know that the total amount collected is $200.30, so the equation becomes:
x + (x + $12.80) + 3x = $200.30
Now, let's combine like terms:
5x + $12.80 = $200.30
Next, we'll isolate the variable by subtracting $12.80 from both sides:
5x = $200.30 - $12.80
5x = $187.50
To find the value of x, we divide both sides by 5:
x = $187.50 / 5
x = $37.50
So, Lia collects $37.50.
Phil collects $12.80 more than Lia, so Phil collects:
$37.50 + $12.80 = $50.30
Cam collects 3 times as much as Lia, so Cam collects:
3 * $37.50 = $112.50
Therefore, Lia collects $37.50, Phil collects $50.30, and Cam collects $112.50.