Answer:
Mary's age = 11 years old
Jane's age = 13 years old
Explanation:
M + J = 24 ⇒ eq. 1
3(M-4) = 2(J-4) + 3 ⇒ eq. 2
M = Mary's age
J = Jane's age
then:
from the eq. 2
3*M + 3*-4 = (2*J + 2*-4) + 3
3M - 12 = 2J - 8 + 3
3M - 12 = 2J - 5
3M = 2J - 5 + 12
3M = 2J + 7 ⇒ eq. 3
From the eq. 1:
M = 24 - J ⇒ eq. 4
replacing eq 4 in eq 3
3(24-J) = 2J + 7
3*24 + 3*-J = 2J + 7
72 - 3J = 2J + 7
-3J - 2J = 7 - 72
-5J = -65
J = -65/-5
J = 13
from the eq. 4
M = 24 - J
M = 24 - 13
M = 11
Check:
from te eq. 2
3(M-4) = 2(J-4) + 3
3(11-4) = 2(13-4) + 3
3*7 = (2*9) + 3
21 = 18 + 3
