Question

Yosief and Datan are playing soccer. Right this moment, if Yosief have 5 goals more than Datan he will have double Datan's, and if Yosief had 7 goals less he will have half the goals of Datan. How many goals does Yosief have right this instance moment?

Answer 1

Yosief has `11` goals

Explanation:

My understanding of the question:

If Yosief had 5 more goals than he currently has, then he would have double the number of goals that Datan has.
If Yosief had 7 fewer goals than he currently has, then he would have half the number of goals that Datan has.

If this interpretation is incorrect then the answer (above) and the derivation (below) will be incorrect.

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Let `y` be the number of goals Yosief currently has
and `d` be the number of goals that Datan currently has.

The given statements, converted into algebraic form would be:

[1]`color(white)("XXX")y+5=2xxd`

[2]`color(white)("XXX")y-7=1/2xxd`

Subtracting [2] from [1], we get
[3]`color(white)("XXX")12=3/2d`

the simplifying:
[4]`color(white)("XXX")3d =24`

[5]`color(white)("XXX")d=8`

Substituting `8` for `d` back in [1]
[6]`color(white)("XXX")y+5=2xx8`

[7]`color(white)("XXX")y=16-5=11`

Giving as a final result `d=8` and `y=11`

Answer 2

Is this question correct?

Explanation:

Let the number of goals by Yosief be `y`
Let the number of goals by Datan ne `d`

`color(blue)("Breaking the question down into its component parts:")`

`color(red)("Right this moment.....")`
if Yosief hase 5 more goals than Datan:`""->y=5+d`..Equation(1)

he will have :`" "->y=5+d=?`

double Datan'es:`" "->y=5+d=2d" "`.......................Equation(2)

'.......................................................................................
and if Yosief had 7 goals less:`" "->y-7`
he would have:`" "y-7=?`
halfe the goals of Datan:`" "->y-7=d/2" "`....................Equation(3)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the value of "y" at this moment")`

Write equation(2) as:

`5+d=2d`

`=>2d-d=5`

`color(purple)(=>d=5)`

Still using equation (2)

`y=5+d=2d" "->" "y=2d`

Substitute `d=5`

`y=2(5)=10`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
There is a contradiction in the construct leading up to equation(3)

Given that `d=5` from equation(2)

`y-7=d/2" "->" "y-7=5/2`

`y=7+2 1/2" "color(red)(larr" You can not have "1/2" of a goal")`