Question

question 10 a father is 25 years older than his son. the quotient of the fathers current age and his sons current age is 6. how old are the father and son now? let x be the current age of the son, and y be the current age of the father. fill in the blanks to complete two equations that model the situation. then find the current ages of the father and the son. (fill each blank with a variable, integer, or math operation.) equation 1: x = \square -25 equation 2: y \div \square = \square fathers current age: \square sons current age: \square

Explanation:

Step1: Define Equation 1

The father is 25 years older than the son, so rearranging gives the son's age as father's age minus 25.
$x = y - 25$

Step2: Define Equation 2

The quotient of father's age to son's age is 6.
$y \div x = 6$

Step3: Substitute x into Equation 2

Replace $x$ with $y-25$ in Equation 2.
$y \div (y - 25) = 6$

Step4: Solve for y

Rewrite division as fraction, then isolate y.

$$\frac{y}{y-25}=6 \\ y = 6(y-25) \\ y = 6y - 150 \\ 5y = 150 \\ y = 30$$

Step5: Solve for x

Substitute y=30 into Equation 1.
$x = 30 - 25 = 5$

Answer:

Equation 1: $x = \boldsymbol{y} -25$
Equation 2: $y\div \boldsymbol{x} = \boldsymbol{6}$
Father's current age: $\boldsymbol{30}$
Son's current age: $\boldsymbol{5}$