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Three students x,y and z share a sum of money in the ratio of 6:3:1. x had $480 more than y. Determi

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Submitted : 2018-06-14 07:40:16    Popularity:     

Tags: money  ratio  sum  students  share  

Three students x,y and z share a sum of money in the ratio of 6 : 3 : 1. x had $480 more than y. The amount each student received: x : $960, y : $480

Answers:

Three students x,y and z share a sum of money
in the ratio of 6 : 3 : 1.
x had $480 more than y.
The amount each student received:
x : $960, y : $480 and z : $160.

Note. ratio 6 : 3 : 1 is made up of 6 + 3 + 1 = 10 Parts

x = 6 parts
y = 3 parts
z = 1 part

Ignoring z, ratio x : y = 6:3 or 2:1
x is twice as big as y:
x = 2y
x - 2y = 0

and
x = y + 480
x - y = 480

Make a simultaneous equation:

x - 2y = 0
x - y = 480

eliminate x by subtracting top from bottom:
y = 480

You can now substitute y = 480 into x - y = 480
x - 480 = 480
x = 960 = 6 parts

y = 480 = 3 parts
z = 480/3 = 1 part
z = 160

X = $960
y =- $480
z = $ 160

Three students, x,y and z, share a sum of money
in the ratio of 6 : 3 : 1.
If x had $480 more than y,
the amount student x received was $960,
the amount student y received was $480 and
the amount student z received was $160.

x:y = 6:3
x/y = 2
x = y + 480
Solve the system of equations.
x = 2y
2y = y + 480
y = 480
x = 960
z = 480/3 = 160

x:y:z=6:3:1
=>
x/6=y/3=z
=>
(y+480)/2=y
=>
y= $480
x= $960
z= $160

x= $288, y= $144, z=$48

x : y : z → 6 : 3 : 1


x/y = 6/3

x/y = 2

x = 2y → given that x had $480 more than y: → x = y + 480

y + 480 = 2y

→ y = 480


Recall: x = 2y

→ x = 960


y/z = 3/1

y/z = 3

3z = y → we’ve just seen that: y = 480

3z = 480

→ z = 160

Let the shares befor x,y and z be 6k, 3k and k
Since x has $480 more than y it means
6k- 3k= 480 i.e. k= 480/3=160
Hence share of x=6k=6* 160= $ 960
Share of y=3k=3* 160= $ 480
Share of z=k=$ 160

Think of the amounts as follows:
X has 6k of the total
Y has 3k of the total
Z has k of the total

X has 480 more than y:
6k = 3k + 480
3k = 480
k = 480/3
k = 160

Now you can figure out the individual amounts:
X : 6k --> 6(160) = $960
Y : 3k --> 3(160) = $480
Z : k --> $160

Answer:
$960, $480 and $160, respectively for X, Y and Z.

x has 6/3 of what y has
x = 2y
x has $480 more than y
x = 480 + y
Since x = x, 2y = 480 + y
y = 480
x = 2y = 960
x = 6z
z = 160



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