define variable, create equation, and solve (written below)

Question

Jessica is six times as old as Sophie, who is two years older than Lucas. In six years, Jessica will be four times as old as Lucas. How old is Jessica 

 

 

Answer 1

let j = Jessica; s = Sophie; L = Lucas

Here's what we know:

j = 6s

s = L + 2 → L = s - 2

j + 6 = 4(L + 6)

 

Distribute:

j + 6 = 4L + 24

Insert the value of s-2 for the variable L:

j + 6 = 4(s - 2) + 24

Distribute again:

j + 6 = 4s - 8 + 24

Combine like terms:

j + 6 = 4s + 16

Isolate j:

j = 4s + 10

 

Insert the value of 6s for the value of j:

6s = 4s + 10

isolate s:

2s = 10

s = 5

 

Now to solve for other people:

j = 6 * 5

j = 30

 

L = 5 - 2

L = 3

 

Check answer:

30 + 6 = 4(3 + 6)

36 = 4 * 9

36 = 36

 

so Jessica is currently 30 years old.