SOLUTION: Mrs. garcia is 1 year less than 3 times as old as her daughter. Seven years from now, she will be 4 years morethan twice as old as her daughter will be then. find both their age

Question 543751: Mrs. garcia is 1 year less than 3 times as old as her daughter. Seven years from now, she will be 4 years morethan twice as old as her daughter will be then. find both their ages using substitution or elimination please show your work
Thank you
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let g = Mr's G's present age
Let d = daughter's present age
:
Write an equation for each statment
:
"Mrs. garcia is 1 year less than 3 times as old as her daughter."
g = 3d - 1
:
"Seven years from now, she will be 4 years more than twice as old as her daughter will be then."
g + 7 = 2(d+7) + 4
g + 7 = 2d + 14 + 4
g + 7 = 2d + 18
g = 2d + 18 - 7
g = 2d + 11
Substitute (3d-1) for g, (from the 1st equation)
3d - 1 = 2d + 11
3d - 2d = 11 + 1
d = 12 yrs is daughter's present age
:
Find g
g = 3(12) - 1
g = 35 yrs is Mrs G's present age
:
:
Confirm this in the statement
"Seven years from now, she will be 4 years more than twice as old as her daughter "
35 + 7 = 2(12+7) + 4
42 = 2(19) + 4
42 = 38 + 4; confirms our solutions

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