Question

la un joc pe calculator, trei copii au castigat inpreuna 780 de puncte. Al doilea copil a castigat de 3 ori mai multe puncte decat primul si inca 8 puncte, l treilea copil a castigat de patru ori mai multe puncte decat primul doi la un loc . Cate puncte a castigat fiecare copil

Answer 1

The number of points won by the first child was 37 points

The number of points won by the second child was 119 points

The number of points won by the third child was 624 points

Explanation:

The question in English is

In a computer game, three children won together 780 points. The second child gained 3 times more points than the first and 8 more points, the third child gained four times more points than the first two in one place. How many points did each child earn

Let

x ----> number of points won by the first child

y ----> number of points won by the second child

z ----> number of points won by the third child

we know that

three children won together 780 points

so

`x+y+z=780` ----> equation A

The second child gained 3 times more points than the first and 8 more points

`y=3x+8` ----> equation B

the third child gained four times more points than the first two in one place

`z=4(x+y)` ----> equation C

Solve the system by substitution

step 1

substitute equation B in equation C

`z=4(x+3x+8)`

`z=16x+32` ----> equation D

step 2

substitute equation D and equation B in equation A

`x+(3x+8)+(16x+32)=780`

step 3

solve for x

`20x+40=780\\20x=740\\x=37`

step 4

Find the value of y

`y=3(37)+8=119`

step 5

Find the value of z

`z=16(37)+32=624`

therefore

The number of points won by the first child was 37 points

The number of points won by the second child was 119 points

The number of points won by the third child was 624 points