A sum of money is divided amongst Farah, Shaiyara and Zahin in the ratio 10: 7: 5. If Shaiyara gets $20 more than Zahin, find the total sum of money shared and the amount
Farah gets.

Answers:

Explanation:

The money is divided in the ratio 10:7:5

This means that

for some positive real number x.

Since Shaiyara gets $20 more than Zahin, we can say,

S = Z+20

Let's plug in S = 7x and Z = 5x and solve for x

S = Z+20

7x = 5x+20

7x-5x = 20

2x = 20

x = 20/2

x = 10

Therefore,

The ratio F:S:Z becomes 100:70:50 which reduces fully to 10:7:5 after dividing all three parts by the GCF 10.

The total sum of money shared is 100+70+50 = 220 dollars and Farah gets $100 of that total.

  5.   y=6; de=7; fg=8

  6.   x=4.2; jl=14.2; mn=13

step-by-step explanation:

when chords cross inside a circle, the product of the segment lengths is a constant.

5. dh×eh = fh×gh

  y = gh = dh×eh/fh = 3×4/2 . . . divide by the coefficient of gh

  y = 6

of course, the total chord length is the sum of the lengths of its segments.

  de = dh +eh = 3+4 = 7

  fg = fh +gh = 2+6 = 8

6. this problem works the same way as the previous one.

  x = lk = mk×nk/jk = 6×7/10 = 4.2

  jl = jk +lk = 10 +4.2 = 14.2

  mn = mk +nk = 6 +7 = 13

comment on chords and secants

you can think of the points h (problem 5) and k (problem 6) as points where the chords meet. a chord is part of a secant line, a line that intersects the circle in two points. one can also consider these points (h or k) to be the points where the respective secant lines meet.

then, the product that is a constant is the product of the distance from the meeting point (h or k) to one circle intersection with the distance from that meeting point to the other circle intersection. for problem 5, the constant is the product hd×he = hf×hg.

it turns out that this rule regarding the products of lengths to points of intersection is also true when the secants intersect outside the circle.

that is, you only need to remember one rule to work both kinds of problems.

answer: what equations are there

step-by-step explanation: