Rhonda has 12 more marbles than Douglas has. Douglas has 6 more marbles than Bertha has. Rhonda has 2 times the number of marbles as Bertha has. How many marbles does Douglas have? Help please. Thank you.
+33653 R = D + 12 (1)
D = B + 6 (2)
R = 2*B (3)
Put (3) into (1): 2*B = D + 12 (4)
Rewrite (2) as B = D - 6 and put this into (4): 2*(D - 6) = D + 12
So: 2D - 12 = D + 12
Subtract D from both sides and add 12 to both sides to get: D = 24
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R = the amount of marbles rhonda has
D = same for douglas
B = .. and bertha
The first step I like to take when solving these kinds of problems, is to define the relation between the variables (that is B, R and D). So:
Ronda has 12 more than douglas gives us: R = D+12
Douglas has 6 more than Bertha: D = B+6
Ronda has 2 times berthas marbles: R = 2*B
To solve an equation with two unknown variables (all three above), we need two different equations that contains said two variables. Since we don't have that, we need to create another. I'm going to use D = B+6 as my starting point, and will now try to create another equation that contains only D and B, using the remaining two equations.
The other equation that contains D is R = D+12. Using the only remaining equation, R = 2*B, i can re-write the first equation to: 2*B = D+12
We now have two equations that describe the relation between the marbles of Douglas and Bertha in two different ways!
1) D = B+6
2) 2*B = D+12
If i can manage to replace the B in 1) with some numbers and the variable D, i will be able to find out how many marbles good ol' Douglas has.
2*B = D+12 gives me that B = (D+12)/2
The B in D = B+6 is replaced with (D+12)/2 which gives me:
D = (D+12)/2 +6 --> D = 0.5D+6 +6 --> D = 0.5D+12.
I solve D = 0.5D+12 by subracting 0.5D on both sides --> 0.5D = 12, and then i divide both sides by 0.5 --> D = 24
Answer: Douglas has 24 marbles.
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