# math - help immediately ?

I substitute for high school math, and I was given this package by the teacher, but I don't understand these three questions. Can somebody help me explain. I know how to do it, but cannot explain it.

Point P is on Line Segment AB. AB = 20 and AP / PB = 5 / 3. How long is AP?

The ratio of 2k - 7a to 3k + a = 3 / 2, then the ratio of k to a is ......?

A study showed that 68% of men and 59% of women voted in favour of Mr.Potus. If everyone voted (all the men and women), and 66% of the people voted yes. What is the ratio of men to women?

Relevance

(i) AP+PB=20

AP/PB=5/3

Therefore, 3AP=5PB, AP=5PB/3

Substitute in AP+PB=20

5PB/3+PB=20

Mulitply by 3 throughout, 5PB+3PB=60

8PB=60

PB=60/8=15/2=7.5

AP=5/3*PB=5/3*15/2=25/2=12.5.

(ii) second question

(2k-7a)/(3k+a)=3/2

Multiply by (3k+a) throghout

(2k-7a)=3/2*(3k+a)

2(2k-7a)=3*(3k+a)

4k-14a=9k+3a

4k-9k=14a-3a

-5k=11a

k/a=-11/5

Answer: The ratio of k/a is -11/5

(c) Let there by x men and y women

the total people voted = total men + total women = x+y

66% voted yes i.e 0.66(x+y) voted yes

68% of men voted = 0.68x

59% of women voted = 0.59y

the total people voted in favor of Mr. Potus =0.68x+0.59y

But this is also equal to 0.66(x+y)

Therefore, 0.68x+0.59y=0.66(x+y)

0.68x+0.59y=0.66x+0.66y

0.68x-0.66x=0.66y-0.59y

0.02x=0.07y

x/y=0.07/0.02=7/2=3.5

Answer: The ratio of men to women is 3.5.

Enjoy!!

the mathguru!!

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• 1. line segment of total length 20. Place a point somewhere in the line segment, so that the ratio of the two new line segments is 5/3. Solve for the length of the two new line segments.

5/3 = 5x / 3x = 5x:3x

5x + 3x = 20, x = 20/8.

so the two lengths are 5(20/8) and 3(20/8)

2. you have (2k - 7a) / (3k + a) = 3/2 and you want to know k/a

cross multiply (think that's what it's called).

(2k - 7a)(2) = (3k + a)(3)

now distribute.

4k - 14a = 9k + 3a

move the k's to one side and the a's to the other.

-17a = 5k

k = (-17/5)a or the ratio of k/a = -17/5

3. let the number of men = x and the number of women = y

there are a total of x+y people, and the amount of people is equal to the amount of votes.

Mr. Potus won 66% of the total vote, or .66(x + y)

.68x + .59y = .66(x + y)

distribute and then move the x's and y's to different sides.

.68x + .59y = .66x + .66y

.02x = .07y

x = .07y/.02 or 7/2y

so the ratio is 7 men to 2 women.

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• for the first one: so if the line is 20 units long and ap is 5/(5+3) so 5/8 the length of ab then 5/8 * 20 = 12.5 units.

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