Question

23. Samantha, lauren, and jerry own shares of the same stock with a total value of $7,650. If Samantha owns fifty shares, Lauren owns seventy shares, and Jerry owns thirty shares, what is the value in dollars of Lauren's stock?

24. How old is David if his age 6 years from now will be twice his age 7 years ago?

25. Three years ago Jane was one-half as old as she will be 2 years from now. What is Jane's present age?

Answer 1

26. A geologist collected 13 rocks that have exactly the same weight. If 9 of these rocks with an additional 5-ounce weight at one end of a balance-scale can balance the remaining rocks and a 23-ounce weight at the other end of the scale, what is the number of ounces in the weight of one of these rocks?

27. Twice the sum of a number and 9 is the same as four times the difference obtained when 6 is subtracted from the number. What's the number?

30. Find four consecutive odd integers such that the sum of three times the second integer and the last integer is 104

31. Find four consecutive integers whose sum is 15 less than 5 times the first.

32. A man mixes 12 pounds of peanuts selling at $1.25 a pound with cashew nuts selling at $1.80 a pound. How many pounds of cashew nuts should be used in order to produce a mixture that sells for $1.50 a pound?

33. Find three consecutive Integers such that the sum of the first integer and three times the last integer is 20 less than 5 times the second integer.

34. Find three consecutive odd integers such that five times the sum of the first and third integers exceeds four times the sum of the second and last integers by 14.

35. Two angles are complementary. The measure of one angle is 5 less than four times the measure of the other angle. Find the number of degrees in the measure of the larger of the two complementary angles.

Best Answer Gets: Medal, Fan, and other OpenStudy Goodies xD

Answer 2

For 23) If Samantha owns fifty shares, Lauren owns seventy shares, and Jerry owns thirty shares, what is the value in dollars of Lauren's stock?
They have 70+50+30 = 150 shares with a value of $7650
So each share would be equal to $7650/150= $51

Now I guess you can solve the question by yourself :)

Answer 3

to take out shares u just do following
7,650*50/150
7,650*70/150
7650*30/150

Answer 4

24) How old is David if his age 6 years from now will be twice his age 7 years ago?
Let's say x being David's current age

His age six years from now: x + 6
His age seven years ago: x- 7

Put that together and solve: x+6 = x-7

Answer 5

25) Three years ago Jane was one-half as old as she will be 2 years from now. What is Jane's present age?

Let's say y is Jane's current age.
Three years ago: y -3
Jane was one-haft as old as she will: (y - 3)*(1/2)
be 2 years from now: y + 2

Put that together
y-3 = (y-3)*(1/2)
and solve.

Answer 6

26) A geologist collected 13 rocks that have exactly the same weight. If 9 of these rocks with an additional 5-ounce weight at one end of a balance-scale can balance the remaining rocks and a 23-ounce weight at the other end of the scale, what is the number of ounces in the weight of one of these rocks?

Let x be the weight of 1 rock

If 9 of these rocks with an additional 5-ounce weight at one end of a balance-scale: 9x + 5
the remaining rocks and a 23-ounce weight at the other end of the scale: (13-9)x + 23

Put them together and solve
9x+5 = 4x + 23

Answer 7

27. Twice the sum of a number and 9 is the same as four times the difference obtained when 6 is subtracted from the number. What's the number?

Let the number be x.

Twice the sum of it and 9: 2(x+9)
is the same as four times the difference obtained when 6 is subtracted from the number
4(x-6)

Put them together and solve.
2(x+9) = 4(x-6)

Answer 8

30. Find four consecutive odd integers such that the sum of three times the second integer and the last integer is 104

Find four consecutive odd integers
Let the first of be x
The four consecutive odd integers would be x, x+2, x+4, x+6

Sum of 3 times the 2nd integer & the last integer = 104
3(x+4) + (x+6) = 104

Solve for x then plug it into these four algebric representation to find those 4 cons. odd integers.

Answer 9

31. Find four consecutive integers whose sum is 15 less than 5 times the first.

Same as above

Let x be the first of the consecutive integers we are looking for.
x, x+1, x+2, x+3
Sum is 15 less than 5 times the first
5x -15 = x+(x+1)+(x+2)+(x+3)

Solve for x and find the three other numbers.

Answer 10

32. A man mixes 12 pounds of peanuts selling at $1.25 a pound with cashew nuts selling at $1.80 a pound. How many pounds of cashew nuts should be used in order to produce a mixture that sells for $1.50 a pound?

Here how it goes,
Let x be the number of pounds of cashew nuts.
($1.25 * 12)+($1.8x) = (12+x) * ($1.5)

What this means, is that the price of 12 pounds of peanuts + the price of cashew nuts equals to $1.50 times the total number of pound in the mixture.

Answer 11

33. Find three consecutive Integers such that the sum of the first integer and three times the last integer is 20 less than 5 times the second integer.

Same same problem, let's see if you can solve this by yourself ;D

Answer 12

34. Find three consecutive odd integers such that five times the sum of the first and third integers exceeds four times the sum of the second and last integers by 14.

Same thing again.

35. Two angles are complementary. The measure of one angle is 5 less than four times the measure of the other angle. Find the number of degrees in the measure of the larger of the two complementary angles.

Angle 1 + Angle 2 = 90, for the first sentence.

Let the first angle be x and the other one y
x = 4y - 5

And we know that x + y = 90

By substitution, you would be able to solve it and find the larger of the two complementary angles.

That's all :)

Answer 13

Wow, thank you very much.