The sum of the ages of two sisters, Mary and Jane, is 24 years old. four years ago three times Mary's age 3 years ago more than twice Jane's age determine the current age

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

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