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Can someone help me with this algebra problem?
Leo,Ian and Mia were born in the same date in different years. Leo's age is Mia's age squared + Ian's age squared. When Mia was born, Ian's age was one-ninth of Leo's. Five years from now, Ian's age + Mia's age will be 16/25 of Leo's age. Find their ages.
1 Answer
- SqdancefanLv 74 years ago
L = M^2 +I^2
(I -M) = (L -M)/9
I +M +10 = 16(L+5)/25
Solve the linear equations for L
.. 9(I -M) +M = L . . . . . . . . . . from the first linear equation
.. 9I -8M = L
.. 25(I +M +10)/16 = L +5 . . . from the second linear equation
.. 25/16I +25/16M +85/8 = L
Equate these and find the relation between M and I.
.. 25(I +M) +170 = 16(9I -8M)
.. 25I +25M +170 = 144I -128M
.. 153M +170 = 119I
Using the 2nd degree expression for L along with the simplified first linear equation, we get two equations in two unknowns:
.. I^2 +M^2 -9I +8M = 0
.. 153M +170 = 119I
It is convenient to solve these graphically to find I = 4, M = 2. Then
.. L = 9*4 -8*2 = 20
Leo's age is 20,
Ian's age is 4,
Mia's age is 2.
Source(s): https://www.desmos.com/calculator/5nvi6hahhv
