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
Submitted : 20180614 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
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


Article Source:
www.Aphotolog.Com
Answer Questions