Answer: 600
Explanation:
First, let's define our variables for this problem:
D = # of points that Dan scored.
E = # of points that Eric scored.
F = #of points that Frank scored.
We know that:
"Dan scored 6/10 of the points that the three boys scored."
D = (6/10)*(D + E + F)
"Eric scored 7/10 of the remaining"
In this case, the remaining refers to (1 - (6/10))*(D + E + F) = (4/10)(D + E + F)
Then:
E = (7/10)*(4/10)*(D + E + F)
And we also know that:
F = 120
Then we have a system of 3 equations:
D = (6/10)*(D + E + F)
E = (7/10)*(4/10)*(D + E + F) = (28/100)*(D + E + F)
F = 120
To solve this, the first step is try to reduce the number of variables, then we can just replace the 3rd equation into the other two:
D = (6/10)*(D + E + 120)
E = (28/100)*(D + E + 120)
Now let's try to isolate the variable E in the second equation:
E = (28/100)*D + (28/100)*E + 36.6
E - (28/100)*E = (28/100)*D + 36.6
E( 1 - 28/100) = (28/100)*D + 36.6
E*(72/100) = (28/100)*D + 36.6
E = (100/72)*((28/100)*D + 36.6) = (28/72)*D + 46.666...
Now let's replace this in the other equation:
D = (6/10)*(D + 120 + (28/72)*D + 46.666...)
Let's solve this for D.
D = (6/10)*(D*(100/72) + 166.666) = 100 + D*(47/72)*(6/10)
D - D*(100/72)*(6/10) = 100
D*(1- (100/72)*(6/10) ) = 100
D = 100/((1- (100/72)*(6/10) ) = 600
Dan scored 600 points