Modeling with equations riddle. A father said that sevens years ago, he was eleven times as old as his daughter. Now he is four times as old as she is. How old is the father?

Ayanna Goodman

Ayanna Goodman

Answered question

2022-11-13

Modeling with equations riddle
A father said that sevens years ago, he was eleven times as old as his daughter. Now he is four times as old as she is. How old is the father?
Can this be solved as a system of equations? I am stuck with this problem because I don't think that I am properly setting up the model.
F a t h e r s A g e 7 = 11 d a u g h t e r s a g e
4 d a u g h t e r s a g e = F a t h e r s a g e

Answer & Explanation

Biardiask3zd

Biardiask3zd

Beginner2022-11-14Added 16 answers

Step 1
Let x = father's age now, and y = daughter's age now. Then:
x 7 = 11 ( y 7 ), and
x = 4 y
Step 2
From this we have: 4 y 7 = 11 y 77 y = 10. Thus: x = 4 ( 10 ) = 40
Dad is 40 years old now.
Jadon Johnson

Jadon Johnson

Beginner2022-11-15Added 3 answers

Step 1
Fathers age = F
Daughters age = D
Seven years ago, he was 11 times as old as his daughter
( F 7 ) = 11 ( D 7 )
Step 2
Now he is four times as old
F = 4 D
You forgot the -7 to the daughter in the first equation

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