Question 601393: here is the problem: three times the number of blue marbles exceeded twice the number of red marbles by 18 Also 5 times the number of blue marbles was 2 less then 6 times the number of red marbles. here is how far I got
3(NB)= 2(nr)+18
5(NB)= 6(nr)-2
nb= 6/5(nr)-2/5
3(6/5nr-2/5) = 2(nr)+18
18/5NR-6/5 = 2NR =18
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Here are comments to your work:
.
3(nb)= 2(nr)+18 <---- correct (I put NB into lower case)
5(nb)= 6(nr)-2 <---- also correct (I put NB into lower case)
nb= 6/5(nr)-2/5 <---- correct (solving second equation for nb)
3((6/5)nr-2/5) = 2(nr)+18 <---- correct (substituting for nb in first equation. Note that I put the 6/5 in parentheses just to ensure the understanding that nr is not in the denominator.
(18/5)nr-6/5 = 2nr + 18 <---- basically correct. Changed the equal sign in front of the 18 to a + sign. Also lower cased the NR for consistency. And put the 18/5 in parentheses.
.
Looks good so far. You can now get rid of the denominator 5 on the left side by multiplying 5 times all terms on both sides to get:
.
18nr - 6 = 10nr + 90
.
Add 6 to both sides and subtract 10nr from both sides:
.
8nr = 96
.
Divide both sides by 8
.
nr = 12
.
Then return to either of the original equations and substitute 12 for nr. Then solve that equation for nb. You will get that nb = 14.
.
Just as a matter of reference, once you got your two equations:
.
3(nb)= 2(nr)+18 and
5(nb)= 6(nr)-2
.
you could have multiplied the top equation (both sides, all terms) by 5 and the bottom equation (both sides, all terms) by 3. This would have given you:
.
15(nb) = 10(nr) + 90 and
15(nb) = 18(nr) - 6
.
Since the left sides are now equal, the right sides must also be equal, which leads to:
.
10(nr) + 90 = 18(nr) - 6
.
Solving this leads to the same equation you got with your method, but it saves messing around with fractions during the solution process. It still gives the same answers.
.
But what you did was fine and right on the mark. You did good, thoughtful work. Keep it up and good luck.
.
|
|
|
