Math Word problems

[Awuah29]

Hi
anyone knows how to set up those problems. Much help appreciated

1.If : x2 –8x = (x-4)/3. What is a value for x that makes this statement true?

2.A worker at an apple orchard is paid $ 15.00 per dozen for the first dozen apples he picks and $ 18.00 per dozen after that. If he picks 78 apples total, then how much will he be paid?

3. Tucker purchased a stock that immediately increased in value by 50%. Th next week it depreciated by 20% and sold the stock for $ 120,000. What was the original purchase price of the stock?

4. If x is positive and x is not equal to zero and y is not equal to zero, then all of the following are the negative except which one.

A. –xy4
B. xsin(5pi/4)
C. –xcos(pi/3)
D. –(xy)2
E. xcos(2pi)


5 If a and b are prime numbers and a x b =x then which of the following could equal x?

A. 23 B. 12 C. 86 D. 77 E. 54

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[BodybldgDoc]

the answer to #5 is D prime numbers 7 * 11 =77

 

[Lonely Sol]

The best way to get the answer for #1 is to plug in the choices.
2. $117
3. $100,000

 

[Mila]

2.A worker at an apple orchard is paid $ 15.00 per dozen for the first dozen apples he picks and $ 18.00 per dozen after that. If he picks 78 apples total, then how much will he be paid?

He gets $15 for the first 12 apples so there are 66 more apples to account for.
There are 5.5 dozen apples in 66.
5.5 times $18(per dozen) is $99.
So that's $99 plus the first $15 (for the 1st dozen) which adds up to $114.

 

[BodybldgDoc]

The answer to #2 is $114. He will be paid 15 for the first dozen and then (5 *18) for the remaining 5 dozens which is 15+90=105 for 72 apples or 6 dozens but he picked 78 in total so he will be paid half of 18 which is 9 for the remaining 6 apples. when you add it all up it ends up as 114. sorry if i did a bad job explaining.

 

[Mila]

3. Tucker purchased a stock that immediately increased in value by 50%. Th next week it depreciated by 20% and sold the stock for $ 120,000. What was the original purchase price of the stock?

When you see one of these problems, it's usually a safe bet to use hypothetical numbers and compare them. And a good idea is to use 100 as your starting number.
So if Tucker purchased a stock at $100, and it increased value by 50%, then it is worth $150.
Then the stock at $150 decreases value by 20%, it will be worth $120. (because $30 is 20% of $150).
It worked out really well in this case because the question gives you $120,000 as your ending price, so you know the starting price had to be $100,000.
Starting with a hypothetical 100 usually works out pretty well in other questions as well.

 

[BodybldgDoc]

Mila has it right. ignore my answer for #4 lol

 

[Mila]

4. If x is positive and x is not equal to zero and y is not equal to zero, then all of the following are the negative except which one.

A. –xy4
B. xsin(5pi/4)
C. –xcos(pi/3)
D. –(xy)2
E. xcos(2pi)

Ok I think **if you have enough time**, the best way to do this is to go through each answer choice. Remember, we don't know if Y is +ve or -ve, but we do know that X is definitely +ve.

A. We don't know if y is positive or negative, but either way once we have Y to the 4th power, it'll become +ve. Then we multiply by +ve X still leaving us with a +ve number... we add in the -ve sign and now we have a -ve number. So this is wrong.

B. sin(5pi/4) falls in the 3rd quadrant and thus is -ve. We multiply that negative number by a positive X, still leaving us with a -ve number. Wrong again!

C. Cos(pi/3) is in the 1st quadrant and is a +ve number. We multiply by X (also a +ve number) leaving us with a positive number still. When we take the -ve sign into account, we now have a -ve number. Not the answer!

D. We multiply X by Y - we don't know if that number is positive or negative, but it doesnt matter because we are squaring it, so either way it'll become positive. We take the -ve sign into account and again we have a -ve number. Wrong!

Finally:

E. Cos(2pi) is zero. X times zero is still zero. This is not a negative number and is thus the right answer!

(If you're lucky and happen to start off with E, then you save a lot of time - either way, do a problem like this last because it can be time consuming and tedious) I hope the explanation made sense - I know it was long...

 

[Chga]

5 If a and b are prime numbers and a x b =x then which of the following could equal x?

A. 23 B. 12 C. 86 D. 77 E. 54

A. No prime numbers multiply to give this
B. not the answer 4 x 3
E. 18 x 3
Now this is confusing
C. 43 x 2
D. 11 x 7

C and D could be the answer b/c they both have a prime number multiplying to become a number listed in the answer Is there a trick or are there multiple answers?

 

[Streetwolf]

1) x^2 –8x = (x-4)/3
3(x^2 - 8x) = x - 4
3x^2 - 24x - x + 4 = 0
3x^2 - 25x + 4 = 0

Quadratic formula: -b +- sqrt(b^2 - 4ac) / 2a

You get: (25 +- sqrt(625 - 48)) / 6
25 +- 24 / 6

You get either ~49/6 = 8.17 or ~1/6 = 0.16

x = 49/6 and 1/6

More exactly, x = 0.163 and 8.17.

Plug it in to check.

2) Solved in another post.

3) Solved in another post.

4) E: cos(2pi) = 1 so you are left with x which is positive.

5) Both C and D are correct. Was one of the two a typo?