word problems and algebra?

Question

5. The nickels and dimes had a value of $5.75. If there were 70 cions in all, how many were nickels?

6. Find thee consecutive integers such that -5 times the sum of the first and the third is 24 greater than 4 times the opposite of the second.

9. Solve for the unknwon variables:RkTk=RnTn, Rk = 6, Rn = 3, Tn-Tk =8

22. 5 1/3x - 3/4 = 7/8

23. 0.03(x-4)=0.02(x+6)

27. simplify by adding like terms:
3x^2a - 5xa + 7x^-2
______ _______
x x^-3a^-1
this is a fraction problem.

^ = to the power of

Answer 1

5. 5x + 10y = 575 and (x+y) = 70
x = 70 - y, so replace in the first equation
5(70-y) + 10y = 575
350 - 5y + 10y = 575
5y = 225
y = 45 dimes
x = 25 nickels

6. x, x+1, x+2
-5 ( 2x + 2 ) + 24 = 4 ( -x -1 )
-10x - 10 + 24 = -4x - 4
6x = 18
x = 3
numbers = 3, 4, 5

9. 6Tk = 3Tn and Tn = 8 + Tk
6Tk = 24 + 3Tk
3Tk = 24
Tk = 8
Tn = 16

22. 5 1/3 = 16/3
16x/3 - 3/4 = 7/8
16x/3 = 13/8
128x = 39
x = 39/128

23. multiply both sides by 100 (for ease)
3x - 12 = 2x + 12
x = 24

27. too poorly formatted to read.

Answer 2

Word problems and algebra?
5. The nickels and dimes had a value of $5.75. If there were 70 cions in all, how many were nickels?
x+y=7=
5x+10y=575
dividing by 5
x+2y=115
x+y=70
subtracting
y=45
substituting x=25

6. Find thee consecutive integers such that -5 times the sum of the first and the third is 24 greater than 4 times the opposite of the second.
let the integers bex-1, x and x+1
the equation
-5(x-1+x+1)=24+4(-x)
-5(2x)=24-4x
-10x=24-4x
-6x=24
x=-4
the integers are -3,-4 and -5


9. Solve for the unknwon variables:RkTk=RnTn, Rk = 6, Rn = 3, Tn-Tk =8
RkTk-RnTn=0
Tn=8+Tk
6*Tk-3(8+Tk)=0
6Tk-24-3Tk=0
3Tk=24
Tk=8
Tn=16

22. 5 1/3x - 3/4 = 7/8
(16/3)x-3/4=7/8
multiplying by 24
128x-18=21
128x=39
x=39/128

23. 0.03(x-4)=0.02(x+6)
multiplying by 100
3(x-4)=2(x+6)
3x-12=2x+12
x=24

27. simplify by adding like terms:
3x^2a - 5xa + 7x^-2
______ _______
x x^-3a^-1
this is a fraction problem
sum not clear

Answer 3

5. 5(70-x) + 10(x) = 575
3.50 - 5x +10x = 5.75
5x = 2.25
x = 45 dimes
so, 70-45 = 25 nickels and 45 dimes
6. -5*(X+X+2) = 24 + -4(X+1)
-5(2x +2) = 24 - 4x - 4
-10x -10 = 20 - 4x
-30 = 6x
x = -5
your numbers are -5, -4, -3
9. don't have the time - at work


22. change to normal fractions
16/3x - 3/4 = 7/8
use common denominator of 24
128/8x - 18/24 = 21/24
128/8x = 39/24
x = 39/24 * 8/128
x = 312/672
x = 21

23. 0.03(x-4)=0.02(x+6)
.03x - .12 = .02x + .12
.01x = .24
x = 24

27. not sure what the question is

Answer 4

Hi there. Call the length "L" and the width "W". We're told that the length of the field is two yards more than its width. So, if we add two yards onto the width, we get the length, i.e. L=W+2. Then we're asked a question involving the area of the field, so let's find an expression for the area. The area of a rectangle is its width multiplied by its length. i.e. AREA=L*W. But we've already found that L=W+2, so the AREA=L*W becomes AREA=(W+2)W (all we've done here is replace L with W+2). So, we've found an expression that gives us the area in terms of just W, the width of the field. We're told that the area of the field is 120yd2. Let's write this as an equation: AREA = 120. Now let's replace AREA with the expression we've just found: (W+2)W=120. Now, let's multiply out the brackets in (W+2)W. This gives W*W + 2*W = W^2 + 2W. So the previous expression becomes: W^2 + 2W = 120. Subtract 120 from both sides to get: W^2 + 2W -120 = 0. Now we have to factorise this to solve this. To factorise an equation like this that involves a W^2, we want to find two numbers that multiply together to make -120 and add together to make 2. After a bit of thought, you'll hopefully be able to see that -10 and 12 fit the bill. Therefore we can rewrite the previous expression as (W+12)(W-10)=0 So, consider when this expression is equal to zero. We've got two things, (W+12) and (W-10), that are zero when multiplied together make zero. This only happens when one of the brackets is zero. This happens when W+12=0 (so W=-12 here) or W-10=0 (W=10 here). So these are the widths we're looking for. Can a field have a negative length? Does that make sense to you? Hopefully it doesn't, because it can't! If I took you to a field and asked you to measure the width of it, I'm sure you wouldn't tell me it was minus twenty yards or whatever! So the answer of "W=-12" that we found just doesn't make sense. There's no problem with our other answer of W=10 though. After all, a field can be 10 yards wide, there's no problem there! The equations you've got at the bottom (from "PROOF" downwards) are just there to demonstrate that your answer actually works. They're the steps that you might go through after solving a problem to check that your answer fits the conditions that the question asked for. So, we've found that W=10 and then going back to the original question, the length was 2 more than the width. So L=10+2 = 12 yards. Therefore the area of the field is width x length = 10 * 12 = 120, which we were told it was! So your answer makes sense! Hurrah! Does that help? Hope so, if not, ask about any specific bits that don't make sense :-)

Answer 5

*Please make sure you copied 6 and 27 correctly.

22) Make 5 1x/3 into an improper fraction:
[5(3) + 1]/3 = 15 + 1/3 = 16/3. Rewrite the equation:

16x/3 - ¾ = 7/8

First: get rid of fractions > take the denominators and multiply them by everything:

3(4)(8)(16x/3) – 3(4)(8)(3/4) = 3(4)(8)(7/8)

Second: cross cancel “like” terms and multiply:

4(8)(16x) – 3(8)(3) = 3(4)(7)
512x – 72 = 84

Third: make sure “x” is on one side. Add 72 to both sides:

512x – 72 + 72 = 84 + 72
512x = 156
512x/512 = 156/512
x = 156/152 and simplify = 39/128

23) First: use distribution by multiplying the outside terms by the inside terms:

0.03x - 0.12 = 0.02x + 0.12

Second: make sure "x" is on one side. Add 0.12 to both sides:

0.03x - 0.12 + 0.12 = 0.02x + 0.12 + 0.12
0.03x = 0.02x + .24

third: subtract 0.02 from both sides:

0.03x - 0.02x = .24
0.01x = .24
0.01x/0.01 = .24/0.01
x = 24

Answer 6

5. nickles- 25 dimes - 45

6. -5, -4, -3

9. Tk=8, Tn=16

22. x=39/128

23. x=24

27 ??