Help with these systems of equations word probs?

Question

I have these system of equation word problems for algebra hw this weekend. However, I'm a little clueless on how to set these up as equations. A little help would be much appreciated.

9. Anya makes 14 baskets during her game. Some of these baskets were worth 2-points and others were worth 3-points. In total, she scored 30 points. Write and solve a system of equations to find how many 2-points baskets she made. For this one, I got 2x + 3y = 30 and 14x + y = 30. Am I on the right track?

10. A library contains 2000 books. There are 3 times as many non-fiction books as fiction books. Write and solve a system of equations to determine the number of fiction and non-fiction books. For this one I have 3x + y = 2000.

11. The chess club has 16 members and gains a new member every month. The film club has 4 members and gains 4 new members every month. Write and solve a system of equations to find when the number of members in both clubs will be equal. I have yet to figure this one out.

Answer 1

Hi,



9. Anya makes 14 baskets during her game. Some of these baskets were worth 2-points and others were worth 3-points. In total, she scored 30 points. Write and solve a system of equations to find how many 2-points baskets she made. For this one, I got 2x + 3y = 30 and 14x + y = 30. Am I on the right track?



x + y = 14 <=number of baskets

2x + 3y = 30 <=points scored



-2(x + y = 14)

2x + 3y = 30



-2x - 2y = -28

2x + 3y = 30

---------------------

y = 2

x = 12



12 2-point shots and 2 3-point shots <==ANSWER



10. A library contains 2000 books. There are 3 times as many non-fiction books as fiction books. Write and solve a system of equations to determine the number of fiction and non-fiction books. For this one I have 3x + y = 2000.



f + n = 2000

n = 3f



f + 3f = 2400



4f = 2400



f = 600

n = 1800



600 fiction and 1,800 non-fiction books <==ANSWER



11. The chess club has 16 members and gains a new member every month. The film club has 4 members and gains 4 new members every month. Write and solve a system of equations to find when the number of members in both clubs will be equal. I have yet to figure this one out.



16 + x = 4 + 4x



12 = 3x



x = 4



In 4 months they will both have 20 members. <==ANSWER



I hope that helps!! :-)

Answer 2

Problem 9.



Let's see.

Let x = the number of 2-point baskets

Let y = the number of 3-point baskets



It's a good idea to write out explicitly what the variables represent so that you can think more clearly about what the problem says and means.



Let's express the conditions in the problem in words first.



"Anya makes 14 baskets during her game."



the number of 2-point baskets + the number of 3-point baskets = 14



This translates into mathematical language as



x + y = 14



"In total, she scored 30 points."



2*(the number of 2-point baskets) + 3*(the number of 3-point baskets) = 30



Or



2x + 3y = 30



Problem 10



DEFINE YOUR VARIABLES. (Pardon me for shouting.)



Let x = the number of non-fiction books

Let y = the number of fiction books



"A library contains 2000 books."



Again in words:

the number of non-fiction books + the number of fiction books = 2000



Now, translate this into mathematics.



"There are 3 times as many non-fiction books as fiction books."



the number of non-fiction books = 3*(the number of fiction books)



Now, translate this into mathematics.



So, think and write the parts of the problem in words first. Then, translate into mathematics.

Later, when you get good at this, you can do some of this in your head. You're not ready for that yet.

Answer 3

9. 20



10. x+y=2000

3x=y

4x=2000

x=500

y=1500



1500 non-fiction

500 fiction



11.16+m=4+4m

12+m=4m

12=3m

m=4



4 months.

Answer 4

Perhaps, but I am not fully convinced