Word Problem and Simplifying problems with variables

[Jessi]

I have one word problem that I'm having trouble with as well as a section of simplifying problems. If someone could show me how to do two of those problems, I should be able to handle the others!

John's mother is eight more than twice his age. His father is three years older than his mother. If all three of the family members have lived for ninety-four years, how old is each person?

(-2a^2x^2 + 3a - x) + (-4a + 2x + 3a^2x^2)

(-y^2 + y - 1) + (6y - 7)

^# = exponent

Thanks so much in advance!

 

[Gene]

John's mother is eight more than twice his age. His father is three years older than his mother. If all three of the family members have lived for ninety-four years, how old is each person?
m=2j+8 His father is three years older than his mother. If all three of the family members have lived for ninety-four years, how old is each person?
m=2j+8. f = m+3. If all three of the family members have lived for ninety-four years, how old is each person?
m=2j+8. f = m+3. j+m+f=94
j+(2j+8)+(2j+8+3)=94

(-2a^2x^2 + 3a - x) + (-4a + 2x + 3a^2x^2)
Gather like terms
a^2x^2+x-a

(-y^2 + y - 1) + (6y - 7)
Gather like terms
-y^2+7y-8

 

[DJ Polaris]

(-2a^2x^2 + 3a - x) + (-4a + 2x + 3a^2x^2)

(-y^2 + y - 1) + (6y - 7)

is this (-2(a^2)(x^2) + 3a - x) + (-4a + 2x + 3(a^2)(x^2))

and for your other problem

John's mother is eight more than twice his age. His father is three years older than his mother. If all three of the family members have lived for ninety-four years, how old is each person?

let m= age of mother
f= age of father
j= age of john

m = 8 + 2j
f = 3 + m
f + m + j = 93

just solve from there
put everything in terms of f or m or whatever you want, solve one thing at a time

 

[Jessi]

I'm sorry - I'm confused on how to get their ages from problems with multiple variables. Like, if I was looking for the mom's age (m = 8 + 2j), how would I get rid of the J?

 

[stapel]

I'm confused on how to get their ages from problems with multiple variables.

Does this mean that you're not familiar with solving systems of linear equations...? Assuming so:

i) Pick a variable for John's age.

ii) Write an expression, in terms of (i), for John's mother's age.

iii) Write an expression, in terms of (ii), for John's father's age.

iv) Sum the variable from (i) and the expressions from (ii) and (iii); simplify.

v) Set equal to the given total of years.

vi) Solve for the variable. Back-solve (using the expressions) for the ages.

Eliz.

 

[Denis]

I'm sorry - I'm confused on how to get their ages from problems with multiple variables. Like, if I was looking for the mom's age (m = 8 + 2j), how would I get rid of the J?

Well, let's see if you can follow this; DJ gave you these 3 equations:
m = 8 + 2j [1]
f = 3 + m [2]
f + m + j = 94 [3]

Substitute [2] in [3]:
3+m + m + j = 94 : that's simple, right?
2m + j = 91
j = 91 - 2m [4] : still with me?

Now take [1]:
m = 8 + 2j
2j = m - 8
j = (m - 8) / 2 [5] : ok?

Now combine [4] and [5]:
91 - 2m = (m - 8) / 2
182 - 4m = m - 8
5m = 190
m = 190/5 = 38 : clear?

Now go back using m=38 to find f and j