Question 623183
Let M = Mary's present age and J = Jane's present age.
1) {{{M = J-7}}} "Mary is 7 years younger than Jane."
2) {{{M+4 = (1/2)(J+4)+1}}} "In 4 year's time, Mary will be one year older than half of Jane's age at that time."
Substitute M from equation 1) into equation 2).
3) {{{(J-7)+4 = (1/2)(J+4)+1}}} Simplify and solve for J.
3a) {{{J-3 = (1/2)J+3}}} Multiply through by 2 to clear the fraction.
3b) {{{2J-6 = J+6}}} Subtract J from both sides.
3c) {{{J-6 = 6}}} Add 6 to both sides.
3d) {{{J = 12}}} Jane is 12 years old.
2a) {{{M = 12-7}}}
2b) {{{M = 5}}} Mary is 5 year old.