Question

can you solve this equation by using simultaneous equations and can you write the method please?

Sarah and Louise have a combined age of 24. Six years ago Sarah was triple Louise's age. What is Sarah and Louise's ages now. Let Sarah be x and Louise be y.

thankyou

Harry

Answer 1

S + L = 24
(S-6) = 3 (L-6)

solve first for L
L = (24 - S)

Multiply second out
S - 6 - 3 L - 18
S = 3 L -12

substitute our L from the first equation in the second equation
S = 3 (24 - S) - 12
S = 72 - 3 S -12
4 S = 60
S = 15
then use the first equation to find L
L = 24 - 15
L = 9

then check
Now
15 + 9 = 24 , yes they add to 24 check
Six years ago
15-6 = 9
9 - 6 = 3
sure enough, 9 is three times 3, check

Answer 2

S + L = 24
(S-6) = 3 (L-6)

solve first for L
L = (24 - S)

Multiply second out
S - 6 = 3 L - 18
S = 3 L -12

substitute our L from the first equation in the second equation
S = 3 (24 - S) - 12
S = 72 - 3 S -12
4 S = 60
S = 15
then use the first equation to find L
L = 24 - 15
L = 9

then check
Now
15 + 9 = 24 , yes they add to 24 check
Six years ago
15-6 = 9
9 - 6 = 3
sure enough, 9 is three times 3, check