Question 232430
Let {{{m}}} = Mother's age now
Let {{{d}}} = Daughter's age now
{{{m - 5}}} = Mother's age {{{5}}} years ago
{{{d - 5}}} = Daughter's age {{{5}}} years ago
given:
(1) {{{m = d + 25}}}
(2) {{{d - 5 = (1/2)*(m - 5)}}}
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This is 2 equations and 2 unknowns, so it's solvable
Multiply both sides of (2) by {{{2}}}
(2) {{{2*(d - 5) = m - 5}}}
(2) {{{2d - 10 = m - 5}}}
(2) {{{2d - m = 5}}}
Subtract {{{d}}} from both sides of (1)
(1) {{{-d + m = 25}}}
Add (1) and (2)
(2) {{{2d - m = 5}}}
(1) {{{-d + m = 25}}}
{{{d = 30}}}
The daughter is 30 years old
check answer:
(1) {{{m = d + 25}}}
(1) {{{m = d + 25}}}
{{{m = 55}}}
(2) {{{d - 5 = (1/2)*(m - 5)}}}
(2) {{{30 - 5 = (1/2)*(m - 5)}}}
(2) {{{25 = (1/2)*(55 - 5)}}}
{{{25 = (1/2)*50}}}
{{{25 = 25}}}
OK