Question

The ages of Max and his father add up to
35 years. Max’s father’s age is the same as five more than the square of Max’s age.
a) Write a system of equations to represent this situation. Define your variables.
b) Solve the system graphically. Are all possible solutions meaningful? Explain.
c) How old are Max and his father?

Answer 1

How do i make the system if equation?

Answer 2

ok so let max's age be A and his father's age be B

Answer 3

Okay

Answer 4

therefore we get two equations:
A+B=35
and
B=A^2 =5
understand?

Answer 5

can we use x and y please it gets confusing if i add something else

Answer 6

sure:
x+y=35
and
x=y^2 =5
where x is the age of Max and y is the age of his father
now thats part a done

Answer 7

sorry x=y^2+5

Answer 8

x=35-y
then i add that into the other equation?
so: 35-y=y^2+5

Answer 9

yup

Answer 10

okay now theres a y and a y^2 .... i should transfer the -y to the other side

Answer 11

sorry x is the age of the father

Answer 12

but yes you do

Answer 13

now solve the equation

Answer 14

ugh confused

Answer 15

theres no x left though

Answer 16

so are we solving for max now?

Answer 17

so after moving everything to one side you should get:
\[y^2 + y - 30 = 0\]

Answer 18

yes solving for Max

Answer 19

I agree

Answer 20

now by solving the equation, you will find that max has two ages: 5 and -6. Because you cannot be -6 years old, Max is 5
Therefore his father is 35-5 = 30yrs old

Answer 21

okay now we factor
_+_=1
_x_=-30
right?

Answer 22

okay can you explain how you did that?

Answer 23

yes so it is =6 and -5
because +6-5=1
and 6 x -5=-30

Answer 24

i should've spent more days factoring :(

Answer 25

it gets very easy when you know how to do it

Answer 26

I know how but the problem is i don't see it right away :( it takes me too long.
thank you, now im going to revise this and try to solve it using the graph cause it tells me to do so

Answer 27

no worries

Answer 28

How do I sketch this?