Two years ago pete was three times as old as his cousin claire. two years before that, pete was four

4 answers
Question:

Two years ago pete was three times as old as his cousin claire. two years before that, pete was four times as old as claire. in how many years will the ratio of their ages be 2 : 1 ?

Answers

6 years if you add the years up and look at the ages

22:11
1. 21:10
2. 20:9
3. 19:8
4. 18:7
5. 17:6
6. 16:5
7. 15:4
8. 14:3
9. 13:2
10. 12:1

Ratios dont add up

4

Step-by-step explanation:

Let P represent Pete's age today.  Let C represent Claire's age today.

2 years ago: P - 2 = 3(C - 2)  ⇒  P - 2 = 3C - 6   ⇒  P = 3C - 4

4 years ago: P - 4 = 4(C - 4)  ⇒  P - 4 = 4C - 16   ⇒  P = 4C - 12


Use substitution to solve the system above:

3C - 4 = 4C - 12

     - 4 = C - 12

       8 = C


Plug in the C-value above into one of the equations to solve for P:

P = 3C - 4

  = 3(8) - 4

  = 24 - 4

  = 20

So, Pete is 20 yrs old today and Claire is 8 years old today


When will Pete be twice as old as Claire?

20 + x = 2(8 + x)

20 + x = 16 + 2x

20       = 16 + x

4          = x

Their ages will have a 2:1 ratio in 4 years.  

P=pete's age now
c=claire's age now

2 year ago pete was 3times as old as his cousin clarie
p-2=3 times (c-2)

also the ratio is 1:3

2 years before that, pete was 4 times as old as claire
p-4=4 times (c-4)

so solve

p-2=3(c-2)
p-4=4(c-4)
distribute
p-2=3c-6
p-4=4c-16

p-2=3c-6
add 2 to both sides
p=3c-4

p-4=4c-16
add 4 to both sides
p=4c-12

so nowe we have
p=3c-4 and p=4c-12
therefor they are equal
3c-4=p=4c-12
3c-4=4c-12
add 12 to both sides
3c+8=4c
subtract 3c from both sides
8=c

subsitute
p-2=3(c-2)
p-2=3(8-2)
p-2=3(6)
p-2=18
addd 2
p=20

so right now, pete is 20 and claire is 8
so we solve by doing
20+what to 8+what=22 to 11
make fraction
and replace what with x
[tex]\frac{20+x}{8+x}= \frac{22}{11}[/tex]
sipmlify 22/11 into 2/1
multiply both sides by 8+x
20+x=[tex]\frac{(2)(8+x)}{1}[/tex]
20+x=2(8+x)
distribute
20+x=16+2x
subtract 16 from both sides
4+x=2x
subtract x from both sides
4=x
the answer is in 4 years

test
20+4=24
8+4=12
24/12=22/11?
2/1=2/1
true

the answer is in 4 years

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