Systems Of Linear Equations Word Problems: A sum of money was divided between A and B
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Okay, well, my first step when setting up a problem is to carefully read it and figure out any variables I might need. In this case, there's going to be two variables at play. Let a be "the amount of money given to person A" and let b be "the amount of money given to person B." Next, I read the problem again to find any clues given. Here, our clues are: "A's share was to B's share as 5 is to 3." and "A's share exceeded 5/9 of the whole sum by $50." Looking just at the first clue, that reads like a ratio problem, so what equation can you create that models that information? Next, what equation can you model with the information from the second clue? (Hint: The "whole sum" will be the total given to A and B. What expression can you use to model that?) Now you have two equations and two variables, and can solve it using whatever method(s) you've learned.
If you need a refresher on these type of problems, try here or here.
If you need a refresher on these type of problems, try here or here.
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Set up the proportion that they've given you. Then multiply through by "B" (and maybe also by "3") to clear the denominator and create a linear equation.
The whole sum is what A and B got together, so that will be A + B. What expression stands for "5/9 of" this sum? (here) What expression stands for "50 more than" 5/9 of this sum? Since A's share is 50 more than 5/9 of the sum, what equation can you create?
You now have two linear equations in two unknowns. Solve the system by whatever method you prefer.
If you get stuck, please reply showing your work, starting with your answers to the above questions. Thank you!
Hello! Thank you both for replying to this thread.
So far I have,
"S" = to the sum of money.
(A + B)/S = 5/3 ~ for my first equation.
Multiplying throughout gives me,
3A + 3B = 5S
Second equation so far I have;
(5/9)S + 50 = A.
I'm not sure how to incorporate B into the second equation. I don't feel like I am that far off.
So far I have,
"S" = to the sum of money.
(A + B)/S = 5/3 ~ for my first equation.
Multiplying throughout gives me,
3A + 3B = 5S
Second equation so far I have;
(5/9)S + 50 = A.
I'm not sure how to incorporate B into the second equation. I don't feel like I am that far off.
I agree with your second equation, but the first one's a bit off. Think about what "the sum of money" really means, compared with what A + B would represent. There's only two people involved in the problem, and they each take some portion of the money. After they both take their money, is there any money leftover? If so, how much? What does this suggest? Incidentally, this also answers your question about how to use B in the second equation.
That takes care of why the first equation is wrong, but now how would you fix it? Perhaps going back to the beginning would help. The problem mentions the ratio of "A's share to B's share..." What expression can you create to model this? As a hint, you got the ratio of "as 5 is to 3" part absolutely correct, so use that as a basis to help you if you're unsure. The problem tells you that these ratios are equal, so that finalizes the equation.
That takes care of why the first equation is wrong, but now how would you fix it? Perhaps going back to the beginning would help. The problem mentions the ratio of "A's share to B's share..." What expression can you create to model this? As a hint, you got the ratio of "as 5 is to 3" part absolutely correct, so use that as a basis to help you if you're unsure. The problem tells you that these ratios are equal, so that finalizes the equation.
Almost. Now your first equation is right, but the second one's wrong. You were very very close before when you had: A = (5/9)S + 50. It seems that my leading questions were too vague, but they were meant to lead you to the conclusion that you don't actually need the variable S at all, because S = A + B. The "sum of the money" is, by definition, the same as A's portion of the money plus B's portion of the money - no one else takes any money and there's none left over after, so their portions together must account for all of the money.
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How does "S" differ from "A + B", being the sum of what A and B received, being the entire amount of money?
How are you getting "(the sum that the shares that were paid out)/(the total that was paid out)" as the proportion (which equals "1", by the way)? Instead, try using what they gave you; namely, that "A's share was to B's share as 5 is to 3".
Again, try using the variables that you already have, which stand for the same thing. Since A + B must equal S, try using A and B instead of S.
Ok, I think I've got it.
(A/B)=5/3
(A+B)5/9 + 50
If someone could finalize this for me that would be greatly appreciated or even give me the answers for A & B so I can continue solving the equation on my own & check my answers.
I have a final tomorrow morning.
Thank you!
(A/B)=5/3
(A+B)5/9 + 50
If someone could finalize this for me that would be greatly appreciated or even give me the answers for A & B so I can continue solving the equation on my own & check my answers.
I have a final tomorrow morning.
Thank you!
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Yes.
No. You're supposed to get an equation, not just an expression. Try following the logic provided earlier:
Actually, us giving you the solutions would help not one whit toward you learning how to do this yourself. Plugging other people's answers in and checking if they're right is a completely different thing from finding the answers yourself.
We've explained the reasoning and essentially given you the equations. Now please show us what you can do. Thank you!
Well, if you're ever unsure of your answers, you can always check them yourself by running the problem "in reverse" and making sure your answers make the given statement(s) true. The problem tells us that "A's share is to B's share as 5 is to 3." So A/B should equal 5/3. Does it? Plugging in your proposed values for A and B gives us: 96.50/27.81 ~= 3.47. That's not 5/3 (~1.67). So, that means the answer's not right, no need to check the other given statement.
Your first equation is 100% right, so let's leave it alone. It's just the second one that's been giving you troubles. Let's go way back to square one and reread the problem to see if we can glean some information from it. "A's share exceeded 5/9 of the whole sum by $50." Right away, we know that A will be more than 5/9 of the sum. But how much more? "By $50." What does it mean for A to be "$50 more than" something? You already know that "5/9 of the whole sum" can be represented by the expression (5/9)(A + B). So, how do you suppose you'd put all this together, to reflect the fact that A is $50 more than (5/9)(A + B)?
Your first equation is 100% right, so let's leave it alone. It's just the second one that's been giving you troubles. Let's go way back to square one and reread the problem to see if we can glean some information from it. "A's share exceeded 5/9 of the whole sum by $50." Right away, we know that A will be more than 5/9 of the sum. But how much more? "By $50." What does it mean for A to be "$50 more than" something? You already know that "5/9 of the whole sum" can be represented by the expression (5/9)(A + B). So, how do you suppose you'd put all this together, to reflect the fact that A is $50 more than (5/9)(A + B)?
My apologize. I really have a hard time constructing word problems but not so much solving them.
A/B = 5/3
A = 5/9(A + 5) + 50
A=5/9(A + 3A/5) + 50
A=5/9((8A)/5) + 50
9A=((40A)/5) + 450
45A = 40A + 2250
5A = 2250
A = 450
450/B=5/3
450 * 3)/5 = $ 270
A = 450
B= 270
Thank you everyone for lending your help! Greatly appreciated.
A/B = 5/3
A = 5/9(A + 5) + 50
A=5/9(A + 3A/5) + 50
A=5/9((8A)/5) + 50
9A=((40A)/5) + 450
45A = 40A + 2250
5A = 2250
A = 450
450/B=5/3
450 * 3)/5 = $ 270
A = 450
B= 270
Thank you everyone for lending your help! Greatly appreciated.
I see no need to apologize for struggling to understand a concept. Not everybody "gets" everything at the same pace. To your credit, you persisted, even when you were struggling, and you did eventually get it. I know many people who would've given up long ago and just wrote it off as "I'm just so bad at math. I'll never figure this out." At this point, my advice is to keep working more word problems until you feel like you've really got it mastered. Word problems aren't going to go away as you continue learning math.
Cheers!
I'm studying for my final math exam tomorrow for an Electrical Engineering program. I can choose one of the three specifications Electronics, Instrumentation, Or Electrical Engineering. I'm leaning towards Electrical or instrumentation. For the Electrical specification I do realize that problems such as these are just the tip of the iceberg for math and word problems.
This is not to say I haven't solved difficult word problems before but when I get stuck I do seem to really get stuck. With that being said, I really am glad I found this site and appreciate you guys giving me a kick in the butt! It's refreshing and this gave me more incentive too try harder.
I'm studying for my final math exam tomorrow for an Electrical Engineering program. I can choose one of the three specifications Electronics, Instrumentation, Or Electrical Engineering. I'm leaning towards Electrical or instrumentation. For the Electrical specification I do realize that problems such as these are just the tip of the iceberg for math and word problems.
This is not to say I haven't solved difficult word problems before but when I get stuck I do seem to really get stuck. With that being said, I really am glad I found this site and appreciate you guys giving me a kick in the butt! It's refreshing and this gave me more incentive too try harder.