Question

How do I write an equation from this word problem?

Jessica has two children: Sophie and Lucas. 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

s=sophies age
l=llucas age
j=jessica's age

j is 6 times of s
j=6s

s is 2 years more than l'
s=2+l

in six years means everybody +6
j+6 is 4 times (l+6)
j+6=4(l+6)


the equations are
j=6s
s=2+l
j+6=4(l+6)

you would subisutte
6s+6=4(l+6)
6(2+l)+6=4(l+6)
undistribute the 2 in each
2(3(2+l)+3)=2(2(l+6))
divide both sides by 2
3(2+l)+3=2(l+6)
distribute
6+3l+3=2l+12
add like terms
9+3l=2l+12
subtract 9 from both sides
3l=2l+3
subtract 2l from both sides
l=3

therefor
s=2+l
s=2+3=5
s=5
6s=j
6(5)=j
j=30



lucas=3
sophie=5
jessica=30