Question

Dan, Eric, and Frank are the leading scorers on their basketball team. Over the course of their high school careers, Dan scored 6/10 of the points that the three boys scored.

If Eric scored 7/10 of the remaining points and Frank scored 120 points, how many points did Dan score?

40 points

280 points

600 points

1,000 points

Answer 1

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