Word Problems: 4 less than 9 times a number is 122, etc

[TorieAndrews]

1) Four less than nine times a number is one hundred twenty-two, find the original number.

2) Copper Wire- A copper conducting wire measures 84 centimeters in length. It is cut into two pieces. The shorter piece is 5 centimeters shorter than the lon piece. Find the length of each piece.

3) Overtime-Maria has a summer job as a tennis instructor to earn her college tuition. She gets paid $6.50 per hour for the first 40 hours and 9.75 for each hour in the week worked more than 40 hours. This summer her goal is to earn at least $338.00 per week. How many hours of overtime per week will she need to achieve her goal?

 

[jwpaine]

Show the work you have done thus far, so that we can help you.

We don't do people's homework here!

 

[Mrspi]

1) Four less than nine times a number is one hundred twenty-two, find the original number.

2) Copper Wire- A copper conducting wire measures 84 centimeters in length. It is cut into two pieces. The shorter piece is 5 centimeters shorter than the lon piece. Find the length of each piece.

3) Overtime-Maria has a summer job as a tennis instructor to earn her college tuition. She gets paid $6.50 per hour for the first 40 hours and 9.75 for each hour in the week worked more than 40 hours. This summer her goal is to earn at least $338.00 per week. How many hours of overtime per week will she need to achieve her goal?

For each of these problems, a very good first step is to NAME things (thanks, Tkhunny!)

for problem 1, you are looking for "the original number." So,

let n = the original number

"9 times the original number" is 9n

"four less than 9 times the original number" is 9n - 4

and "four less than 9 times the original number is 122"....so...
9n - 4 = 122

Ok...solve that for n.

Now, try that same kind of approach on the other problems. If you show us what you try, we can see where it is that you need help.

If you came here looking for complete, worked out solutions to your problems, you came to the wrong place.

 

[TorieAndrews]

I dont ask for anyone to do my home work for me, these are problems that I was stuggling with. But thank you for helping, I will try your approarch and figure the problems out for here

The solution for # 2

n=84-5
n=80

 

[Mrspi]

Ok...let's try the "name things" approach on #2


You have 2 pieces of wire

Let s = "short piece"

The long piece is 5 cm MORE than the short piece, so
long piece = s + 5

Now...the two pieces together must equal the length of the wire they were cut from....

short piece + long piece = total length of wire

s + (s + 5) = 84

Ok...solve that for s....

 

[TorieAndrews]

#2 questions

Oh ok I get it, its not all about adding and subtracting all the time, You just have to
simply in the problem solving format

I will # 3
with the same approach

 

[TorieAndrews]

Oh wait this is a different example. Bare with me, I'm trying to understand the examples in my text book.

 

[Denis]

Oh wait this is a different example. Bare with me, I'm trying to understand the examples in my text book.

...that should be "bear with me", not "bare"

Maria has a summer job as a tennis instructor to earn her college tuition. She gets paid $6.50 per hour for the first 40 hours and 9.75 for each hour in the week worked more than 40 hours. This summer her goal is to earn at least $338.00 per week. How many hours of overtime per week will she need to achieve her goal?

Take your time with these; they only "look" complicated.
Apply the problem to yourself:
if you work 40 hours at $6.50 an hour, that's 40 * 6.5 = $260 ; agree?
Since you need $338, then you're short 338 - 260 = $78 ; ok?
You will work overtime to earn this $78, right?
And you will be paid $9.75 per hour, right?
So the number of hours will be ????
Got it :?: