Five year ago the age of Maya was seven times the age of her son. the age of Maya will be three times the age of her son in 5 years. represent the situation as an equation and draw its graph. find the present age of mother and son.
Answers
Age of maya=40 years
Age of her son =10 years
Answer and explanation:
Let the present age of Maya be x and that of her son be y.
Five years ago,
Maya's age = (x - 5) years
Her son's age = (y - 5) years
According to the question, we have
(x - 5) = 7(y - 5)
x - 5 = 7y - 35
x = 7y - 35 + 5
x = 7y - 30 ------------------------- (i)
In 5 years,
Maya's age = (x+5) years
Her son's age = (y+5) years
Accordingly, we have
x + 5 = 3(y + 5)
x + 5 = 3y + 15
x = 3y + 15 - 5
x = 3y + 10 ----------------------------- (ii)
Subtracting (ii) from (i), we get
x - x = (7y - 30) - (3y + 10)
0 = 7y - 30 - 3y - 10
0 = 4y - 40
4y = 40
y = 40/4
y = 10 years
Putting the value of y in (i), we get
x = 3(10) + 10
x = 30 + 10
x = 40 years
Hence, Maya's age = x = 40 years
Her son's age = y = 10 years
The graph of equations (i) and (ii) is given below
And from the graph, we get the solution as x = 40 and y = 10. (Same as the calculated values).
#SPJ2
