Question

The present age of Madison's Mother is 3 time that of Madison. After 6 1/4 years, the sum of their age will be 53 3/4 years. Find their present ages. (Estimate to the nearest whole number)

Answer 1

Answer:
`10, 31\ \text{years}`

Explanation:

Given

The present age of Madison's Mother is three time that of Madison

Suppose the Present age of Madison is
`x`, so age of her mother is
`3x`

After
`6(1)/(4)\ \text{years}`, the sum of their age will be
`53(3)/(4)\ \text{years}`

`\therefore (x+6(1)/(4))+(3x+6(1)/(4))=53(3)/(4)\\\\\Rightarrow 4x+2* (25)/(4)=(53* 4+3)/(4)\\\\\Rightarrow 4x+(50)/(4)=(215)/(4)\\\\\Rightarrow 4x=(215-50)/(4)\\\\\Rightarrow x=(165)/(16)\\\\\Rightarrow x= 10.31\approx 10`

Madison mother's age
`3x=30.93\approx 31\ \text{years}`