Blushxroses
contestada

There are 5 people standing in a room. Rick is 5 times the age of Mike who is half the age of Larry. Ed is 30 years younger than double Larry and Mike’s combined ages. Daniel is 79 years younger than Rick. The sum of their ages is 271. How old is Daniel? PLEASEEEEE HURRRYYY

Respuesta :

calculista

Answer:

Daniel is 21 years old

Step-by-step explanation:

Let

R ---> Rick's age

M ---> Mike's age

L ---> Larry's age

E ---> Ed's age

D ---> Daniel's age

we know that

The sum of their ages is 271

so

[tex]R+M+L+E+D=271[/tex] ----> equation 1

Rick is 5 times the age of Mike

so

[tex]R=5M[/tex] ----> equation 2

Mike is half the age of Larry

so

[tex]M=(1/2)L[/tex]

[tex]L=2M[/tex] ----> equation 3

[tex]E=2(L+M)-30[/tex]   ----> equation 4

[tex]D=R-79[/tex] ----> equation 5

substitute equation 2, equation 3, equation 4 and equation 5 in equation 1

[tex]5M+M+2M+2(L+M)-30+R-79=271[/tex]

simplify

[tex]10M+2L+R=380[/tex] -----> equation 6

substitute equation 2 and equation 3 in equation 6

[tex]10M+2(2M)+5M=380[/tex]

solve for M

[tex]19M=380\\M=20\ years[/tex]

Find the value of R (equation 2)

[tex]R=5(20)=100\ years[/tex]

Find the value of D (equation 5)

[tex]D=100-79=21\ years[/tex]

therefore

Daniel is 21 years old

Otras preguntas