# Thread: Football club, how many showed up for pratic.

1. ## Football club, how many showed up for pratic.

The football club has pratic one day.
1/4 did powerlifting
2/5 did technical training.
and the remaning 21 did cardio.

How many showed up for pratic this day?

2. ## Re: Football club, how many showed up for pratic.

Let X be the total number that showed up.
"1/4 did powerlifting" That's (1/4)X= X/4 people

"2/5 did technical training." That's (2/5)X= 2X/5 people

"and the remaining 21 did cardio" That's 21 people

The total is X/4+ 2X/5+ 21= X.

Solve that for X. I would start by subtracting X/4 and 2X/5 form both sides. However I think you will find that this is impossible. X does not turn out to be a whole number.

3. ## Re: Football club, how many showed up for pratic.

Originally Posted by HallsofIvy
Let X be the total number that showed up.
"1/4 did powerlifting" That's (1/4)X= X/4 people

"2/5 did technical training." That's (2/5)X= 2X/5 people

"and the remaining 21 did cardio" That's 21 people

The total is X/4+ 2X/5+ 21= X.

Solve that for X. I would start by subtracting X/4 and 2X/5 form both sides. However I think you will find that this is impossible. X does not turn out to be a whole number.

X/4+ 2X/5+ 21= X.

X x 20 /4 + 2X x 20 / 5 + 21 = X

X x 5 + 2X x 4 + 21 = X

5X + 8X + 21 = X

13X + 21 = X

13X - X = -21

12X = -21

12X / 12 = -21 / 12

X = -1.75

Am i on the right track and if soo, wher do i go from her?

4. ## Re: Football club, how many showed up for pratic.

$n$ folks showed up

$\dfrac{n}{4} + \dfrac{2n}{5} + 21 = n$

$\dfrac{5n}{20}+\dfrac{8n}{20} + 21 = n$

$\dfrac{13}{20}n + 21 = n$

$21 = \dfrac{7}{20}n$

$n = 60$

5. ## Re: Football club, how many showed up for pratic.

Originally Posted by Greb
The football club has pratic one day.
1/4 did powerlifting
2/5 did technical training.
and the remaning 21 did cardio.
How many showed up for pratic this day?
Lets find a common denominator: $\frac{1}{4}=\frac{5}{20}~\&~\frac{2}{5}=\frac{8}{ 20}$.
Thus the remaining $21$ form $\frac{7}{20}$ of the whole. So $X=60$.

6. ## Re: Football club, how many showed up for pratic.

Originally Posted by romsek
$n$ folks showed up

$\dfrac{n}{4} + \dfrac{2n}{5} + 21 = n$

$\dfrac{5n}{20}+\dfrac{8n}{20} + 21 = n$

$\dfrac{13}{20}n + 21 = n$

$21 = \dfrac{7}{20}n$

$n = 60$

$\dfrac{13}{20}n + 21 = n$

$21 = \dfrac{7}{20}n$

what happend her?

7. ## Re: Football club, how many showed up for pratic.

Originally Posted by Greb
$\dfrac{13}{20}n + 21 = n$

$21 = \dfrac{7}{20}n$

what happend her?
really?

multiply both sides of the equation by $\dfrac{20}{7}$

8. ## Re: Football club, how many showed up for pratic.

Originally Posted by Greb
$\dfrac{13}{20}n + 21 = n$

$21 = \dfrac{7}{20}n$

what happend her?
$n = 1\cdot n = \dfrac{20}{20}\cdot n$

$\dfrac{13}{20}n + 21 = n$

$\dfrac{13}{20}n + 21 = \dfrac{20}{20}n$

$\dfrac{13}{20}n+21 - \dfrac{13}{20}n = \dfrac{20}{20}n - \dfrac{13}{20}n$ (what you do to one side, you must do to both)

$\cancel{\dfrac{13}{20}n} + 21 - \cancel{\dfrac{13}{20}n} = \dfrac{20-13}{20} n = \dfrac{7}{20}n$

$21 = \dfrac{7}{20}n$

9. ## Re: Football club, how many showed up for pratic.

Originally Posted by romsek

$21 = \dfrac{7}{20}n$

$n = 60$
sorry, i meant to ask for this part. what happend her?

10. ## Re: Football club, how many showed up for pratic.

Originally Posted by Greb
sorry, i meant to ask for this part. what happend her?
Then, as romsek said, multiply both sides by $\dfrac{20}{7}$.