Question

17. a) Ula jest dwa razy młodsza od Oli i o 4 lata starsza od Ali. Razem te trzy

Answer 1

Answer:

Part 17)

Ula's age is 7 years

Ola's age is 14 years

Ali's age is 3 years

Part 18) Zosia's age is 15 years

Part 19) All together are 36 years old

Step-by-step explanation:

The question in English is

17. Ula is twice as young as Ola and four years older than Ali. Together these three girls are 24 years old. How old is each of them?

18. Zosia's father is 3 times older than her and Zosia is 30 years younger than him.

How old is Zosia?

19. Julek and Asia are 6 years older than Michael, but each of them separately is younger than him: Julek by 7 years, Asia by 2 years. How old are they all together?

Part 17)

Let

x ----> Ula's age

y ---> Ola's age

z ---> Ali's age

we know that

Ula is twice as young as Ola

$y=2x$ ----> equation A

Ula is four years older than Ali

$x=z+4$

$z=x-4$----> equation B

Together these three girls are 24 years old.

so

$x+y+z=24$ -----> equation C

substitute equation A and equation B in equation C

$x+2x+(x-4)=24$

solve for x

$4x=24+4\\4x=28\\x=7$

Find the value of y

$y=2(7)=14$

Find the value of z

$z=7-4=3$

therefore

Ula's age is 7 years

Ola's age is 14 years

Ali's age is 3 years

Part 18)

Let

x ----> Zosia's father's age

y ----> Zosia's age

we know that

Zosia's father is 3 times older than Zosia.

so

$x=3y$  ----> equation A

Zosia is 30 years younger than him.

so

$y=x-30$ ----> equation B

substitute equation A in equation B

$y=3y-30$

solve for y

$3y-y=30\\2y=30\\y=15$

therefore

Zosia's age is 15 years

Part 19)

Let

x ----> Julek's age

y ----> Asia's age

z ----> Michael's age

we know that

Julek and Asia are 6 years older than Michael

so

$x+y=z+6$ ----> equation A

Julek is 7 years  younger than Michael

$x=z-7$ ----> equation B

Asia is 2 years  younger than Michael

so

$y=z-2$ -----> equation C

substitute equation B and equation C in equation A

$(z-7)+(z-2)=z+6$

solve for z

$2z-z=6+9\\z=15$

Find the value of x

$x=15-7=8$

Find the value of y

$y=15-2=13$

Adds the ages

$x+y+z=8+13+15=36\ years$

therefore

All together are 36 years old