# problem solving: percentages, number probs, work probs, etc

#### mrs.wright1976

1) A certain sum of money is invested at 10%. Twice that amount is invested at 8%. The total amount of interest from both investments is $91. How much is invested at 8%. 2) The sum of two numbers is 17 and the sum of their square is 145. Find the larger number 3) If 6 men can do a piece of work in 14 days, how many men are needed to do the work in 21 days? 4) The width of a rectangle is 15 feet less than its length, and the perimeter is 210 feet. Find the width 5) Three times the square of a certain positive number exceeds six times the number by nine. Find the number 6) If a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours, the rate of the river and the rate of the boat in still water respectively are ________? 7) The sum of both digits, of either of two two-digit numbers, in whatever order the digits are written, is 9. The square of either of the digits of either number, minus the product of both digits, plus the square of the other digit is the number 21. The numbers are _______? a. 36,63 b. 81, 18 c. 27, 72 d. 45, 54 e. none Please show your work! #### stapel ##### Super Moderator Staff member Unfortunately, the "Read Before Posting" thread, present at the head of so many of the other forums, is missing on this one, so you didn't know better when you flooded the forum with nine or ten questions within minutes, none of them showing any effort. Sorry! As the article in the link (above) explains, this is not a "we do your homework for you" sort of place. This is a tutoring forum. Legitimate tutors help students learn how to do things for themselves, so one of the primary guidelines here is that the student post a representative exercise (not a flood or the entire assignment), and another is that the student show his/her own effort. Note: This is not a paid service, so there are no "employees" waiting on stand-by to provide instant solutions. The tutors are volunteers who surf by when they are able. Please be prepared to wait hours, if not days, for any further replies (especially if no work is shown). Since you have been unable even to attempt any of these exercises, I will guess that you are needing lessons on how to approach these, since you were out sick the week or two that they were covered in class. Unfortunately, we cannot reasonably provide the missing classroom instruction; anything we tried to provide here would be much less complete than your book and the class notes you got from a friend. Fortunately, there are loads of great lessons online, so we can provide you some links. mrs.wright1976 said: 1) A certain sum of money is invested at 10%. Twice that amount is invested at 8%. The total amount of interest from both investments is$91. How much is invested at 8%.
First study percentages, and then learn how to use them in word problems; you can also study specifically about "investment" word problems.

mrs.wright1976 said:
2) The sum of two numbers is 17 and the sum of their square is 145. Find the larger number
I am assuming that you're familiar with variables and solving linear equations. For this exercise, first learn how to translate the words into math, and then study "number" word problems for specifics.

mrs.wright1976 said:
3) If 6 men can do a piece of work in 14 days, how many men are needed to do the work in 21 days?
There are various ways to approach "work" word problems. Did you have a particular method in mind?

mrs.wright1976 said:
4) The width of a rectangle is 15 feet less than its length, and the perimeter is 210 feet. Find the width
First review the geometric formulas, and then study some specifics of "geometric" word problems.

mrs.wright1976 said:
5) Three times the square of a certain positive number exceeds six times the number by nine. Find the number
This one works just like (2).

mrs.wright1976 said:
6) If a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours, the rate of the river and the rate of the boat in still water respectively are ________?
Have you studied systems of linear equations yet? (There are at least two different ways to approach this "distance" word problem, and the method used will vary with what your class has covered.)

mrs.wright1976 said:
7) The sum of both digits, of either of two two-digit numbers, in whatever order the digits are written, is 9. The square of either of the digits of either number, minus the product of both digits, plus the square of the other digit is the number 21. The numbers are _______?
You'll need your translation skills and your "number" problem skills for this one. Let's work on (1) through (6), and your other threads, before getting too bogged down in this one, okay?

Please study the lessons in the links (this shouldn't take more than a few hours), learn the basic terms and techniques, and then attempt the exercises. If you get stuck, please reply showing all of your steps and reasoning so far. Thank you! mrs.wright1976 said:
Actually, that's your job! :wink:

I look forward to hearing from you! Eliz.

P.S. Welcome to FreeMathHelp! #### mrs.wright1976

##### New member
FYI

I am not a student, nor is this homework for me. I would like someone with great diligent to help me with these problems for I am trying to refresh my memory.

#### stapel

##### Super Moderator
Staff member
mrs.wright1976 said:
I am not a student, nor is this homework for me. I would like someone with great diligent to help me with these problems for I am trying to refresh my memory.
So you're saying that you're not in any class, you're doing self-study, and these are the exercises from the end of the chapter you've been reading...? :shock:

If so, and if you still (after having put "great diligent" effort into studying the lessons you've been provided) are still unable even to begin these exercise, I would strongly suggest that you (1) get a different text and (2) hire a tutor to help you work through these concepts.

My best wishes to you in your studies. Eliz.

Staff member

#### Denis

##### Senior Member
Re: problem solving: percentages, number probs, work probs,

mrs.wright1976 said:
4) The width of a rectangle is 15 feet less than its length, and the perimeter is 210 feet. Find the width
Problem is, Mrs W, that if you can't solve something as easy/basic
as that problem, then you need a "teacher", and this site is not a
classroom, no matter what degree of diligence one may have.

#### H8Math

##### New member
i see that this post is old, but i am having trouble figuring out the answers to these questions as well. they are for an employment test i have to take tomorrow. i aced all of the other aptitude tests, but math is just not my strong suit. i'm freaking out about this test :shock: thank you for at least posting where i can obtain the information i need to attempt to figure these problems out. #### H8Math

##### New member
i've been studying number six and the linear equation help provided, but i still don't understand how they relate. i've made them x and y coordinates, i've tried the slope formula & got -4 (not sure whether/how it applies)...

would someone give me a hint as to how systems of linear equations could help me solve this problem? :?:

#### Subhotosh Khan

##### Super Moderator
Staff member
mrs.wright1976 said:
6) If a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours, the rate of the river and the rate of the boat in still water respectively are ________?

There is an intuitive way you can solve the problem. We assume that the speed of the boat in still water is same (up and down the stream) and speed of water is same.

downstream speed = 24 mi/hr

Upstream speed = 10 mi/hr

The difference is 14 mi/hr - so the current speed is (14/2 =) 7 mi/hr

The speed of boat in still water = (24 - 7 = 10 + 7 =) 17 mi/hr

#### Denis

##### Senior Member
H8Math said:
i've been studying number six and the linear equation help provided, but i still don't understand how they relate. i've made them x and y coordinates, i've tried the slope formula & got -4 (not sure whether/how it applies)...
would someone give me a hint as to how systems of linear equations could help me solve this problem? :?:
6) If a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours,
the rate of the river and the rate of the boat in still water respectively are ________?

b = boat's speed, c = current's speed

formula: speed = distance / time

Going downstream, speed is b+c mph : boat's plus current's, ok?
Going upstream, speed is b-c mph : boat's speed id reduced by current's speed, ok?
Using formula:
Downstream: b+c = 72/3 = 24
Upstream: b-c = 60/6 = 10

So the 2 linear equations are:
b + c = 24
b - c = 10
Solve those and you'll get same as Subhotosh.