Question

Mr. Thaxton has two daughters. The sum of their ages is twenty-one. The product of their ages is one hundred ten. How old is Mr. Thaxton's youngest daughter?A.9B.10C.11D.12

Answer 1

Given the question, the following are the solution steps to answer the question.

STEP 1: Represent the two daughters with a variable

Let the first daughter represented with y

Let the second daughter be represented with z

STEP 2: Interpret the statements in the question

`\begin{gathered} \text{From second statement:} \\ y+z=21----\text{equation 1} \\ \text{From third statement:} \\ y* z=110----\text{equation 2} \end{gathered}`

STEP 2: Write out the two gotten equations

`\begin{gathered} y+z=21----(1) \\ yz=110----(2) \\ \end{gathered}`

STEP 3: Make y the subject of the equation 1

`\begin{gathered} \text{Subtract z from both sides} \\ y+z-z=21-z \\ y=21-z \end{gathered}`

STEP 4: Substitute the value for y in equation 2

`\begin{gathered} yz=110 \\ (21-z)z=110 \\ 21z-z^2=110 \\ \text{Subtract 110 from both sides} \\ 21z-z^2-110=110-110 \\ 21z-z^2-110=0 \end{gathered}`

STEP 5: We solve the quadratic equation to get the values of z

`\begin{gathered} 21z-z^2-110=0 \\ \mathrm{Write\: in\: the\: standard\: form}\: ax^2+bx+c=0 \\ z^2+21z-110=0 \\ \text{ Using quadratic formula;} \\ z_(1,\: 2)=(-21\pm√(21^2-4\left(-1\right)\left(-110\right)))/(2\left(-1\right)) \\ 21^2-4(-1)(-110)=\sqrt[]{1}=1 \\ z_(1,\: 2)=(-21\pm\:1)/(2\left(-1\right)) \\ \mathrm{Separate\: the\: solutions} \\ z_1=(-21+1)/(2\left(-1\right)),\: z_2=(-21-1)/(2\left(-1\right)) \\ z_1=(-20)/(-2)=10 \\ z_2=(-22)/(-2)=11 \\ z=10,\: z=11 \end{gathered}`

STEP 6: Get the age of the other daughter

`\begin{gathered} y+z=21 \\ \text{when }z=10 \\ y=21-10=11 \\ \text{When z=11} \\ y=21-11=10 \\ \\ \therefore ages\text{ of the daughters are: }10\text{ years and 11 years} \end{gathered}`

Hence, the age of Mr. Thaxton's youngest daughter is 10 years