Question

Question #41bb8

Answer 1

`"Greg is now 15"`

Explanation:

Questions like this are confusing is because it's hard to know
how to write all those ages.

The trick is to find a way to express each age by going one step at a time.

Let `x` represent the number of years in Susan's age now.

• Susan now . . . . . . . . ..`x` `larr` Susan's age now
• Twice as much . . . . .`2x` `larr` Becca's age now
• 9 years more , , , , , , . `x + 9` `larr` Greg's age now

`color(white)(.............)`———————

Their ages 3 years ago can be expressed like this:

• Susan then . . . . . `x - 3`
• Becca then . . . . `2x - 3`
• Greg then . . . . . .`(x + 9) - 3`

`color(white)(.............)`———————

The problem says:

3 years ago, Becca was 9 less than 3 times Susan's age.

Becca then was 3 times Susan minus 9

`"[ Becca then ] was   [3 times Susan] minus  [ 9 ]"`
`[      2x - 3     ]   =    [            3x          ]   -       [ 9 ]`

`2x - 3 = 3x - 9`
Solve for `x`, already defined as the number of years in Susan's age

1) Subtract `2x` to get all the `x` terms together
`- 3 = x - 9`

2) Add 9 to both sides to isolate `x`
`6 = x`, already defined as the number of years in Susan's age

If Susan is 6, then Greg is 15

Answer:
`"Greg is now 15"`

`color(white)(.............)`———————

Check

See if the list of expressions all work out

• Susan now . . . . . . . . ..`6` `larr` Susan's age now
• Twice as much . . . . .`12` `larr` Becca's age now
• 9 years more , , , , , , `15` `larr` Greg's age now

`color(white)(.............)`———————

• Susan's age then . . . .`x - 3` = `3`
• Becca's age then . . . .`2x - 3` = `9`
• Greg's age then . . . . `(x + 9) - 3` `= 12`

If Greg's age 3 years ago was 12, then his age now is 15.

`Check!`

Answer 2

Greg's age `=24`

Explanation:

To find Greg's age, first find Susan's age.

Susan's age `=x` years

Becca's age in terms of Susan's age from the 1st information
Becca's age `=x xx2=2x`

Becca's age in terms of Susan's age from the second information
3 years ago Susan's age `=x-3`
3years ago Becca's age `=[(x-3)xx3]-9=3x-9-9=3x-18`
Then, What is Bacca's age to-day?
Becca's age to-day =Becca's age three years ago + 3

Becca's age to-day `=[3x-18]+3=3x-18+3=3x-15`

We get Becca's age from two different information.
So, Becca's calculate in two ways must be equal to each other.
Form an equation.

`2x=3x-15`
Solve for `x`
`2x-3x=-15`
`-x=-15`
`x=15`

Susan's age `=15` years.

Greg's age`=`Susan's age `+9`

Greg's age `=15+9=24`

Greg's age `=24`

Answer 3

Greg's age `=24`

Explanation:

Three years ago -

Susan's age `=x`
Becca's age = three times Susan's age less Nine years.
Becca's age `=3x-9`

Becca's age three years ago `=3x-9`

`3x-9` -------Expression (1)

Now

Susan's age `=x+3`
[Susan's age cannot be `x` after three years. She must be three years older than she was three years ago]

Becca's age = two times Susan's age
Becca's age `=(x+3)2=2x+6`

`2x+6` ---------Expression (2)

The two expressions are about Becca's age at two different periods. One cannot be equated with the other unless we make some correction.

Take expression (2)

If Becca's age now is `2x+6`, what could be his age three years back.

Using expression (3) , let us calculate the age of Becca three years ago.

Becca's age three years ago =Becca's age now - 3
Becca's age three years ago `=(2x+6)-3=2x+6-3=2x+3`
Becca's age three years ago `=2x+3`

`2x+3` ----- expression (3)

Now, we have calculated Becca's age in two different ways based on the information given in the problem. So,

Expression (1) must be equal to Expression (2)

`3x-9=2x+3` Solve it

`3x-2x=3+9`
`x=12`

The value of `x` is Susan's age three years ago.

Susan's age `x=12`
Susan's age now `=x+3= 12 +3 = 15`

Greg is 9 years older than Susan.

Greg's age `=15+9=24`

Greg's age `=24`