kisses is five years old than Mikay. The product of their ages four years from n...

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October 2022 1 4 Report

kisses is five years old than Mikay. The product of their ages four years from now is 50. Find their present ages.

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UK2019

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✏️AGES

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$\large\bold{\red{PROBLEM:}}$ Kisses is five years old than Mikay. The product of their ages four years from now is 50. Find their present ages.

$\large\bold{\red{SOLUTION:}}$ Represent x and y as it is Kisses and Mikay's age respectively. Make equations on the given statement.

$\begin{gathered} \begin{cases} \sf x = y + 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \green{(eq. \: 1)}\\ \sf(x + 4)(y - 4) = 50 \: \: \: \: \: \green{(eq. \: 2)}\end{cases} \end{gathered}$

- Substitute x from the first equation to the second equation in terms of y.

$\begin{gathered} \begin{cases} \sf x = y + 5 \\ \sf(y + 5 + 4)(y - 4) = 50 \end{cases} \end{gathered}$

$\begin{gathered} \begin{cases} \sf x = y + 5 \\ \sf(y + 9)(y - 4) = 50 \end{cases} \end{gathered}$

$\begin{gathered} \begin{cases} \sf x = y + 5 \\ \sf {y}^{2} + 5y - 36 = 50 \end{cases} \end{gathered}$

$\begin{gathered} \begin{cases} \sf x = y + 5 \\ \sf {y}^{2} + 5y - 36 - 50 = 0 \end{cases} \end{gathered}$

$\begin{gathered} \begin{cases} \sf x = y + 5 \\ \sf {y}^{2} + 5y - 86 = 0 \end{cases} \end{gathered}$

- Solve the quadratic equation in second equation by using the quadratic formula. Use the positive situation so we talk about ages.

$\begin{gathered} \sf y = \frac{ \text- 5 + \sqrt{ {5}^{2} - 4(1)( \text - 86)} }{2(1)} \end{gathered}$

$\begin{gathered} \sf y = \frac{ \text- 5 + \sqrt{ 25 - 4(1)( \text - 86)} }{2} \end{gathered}$

$\begin{gathered} \sf y = \frac{ \text- 5 + \sqrt{ 25 - 4(\text - 86)} }{2} \end{gathered}$

$\begin{gathered} \sf y = \frac{ \text- 5 + \sqrt{ 25 - ( \text - 344)} }{2} \end{gathered}$

$\begin{gathered} \sf y = \frac{ \text- 5 + \sqrt{ 25 + 344} }{2} \end{gathered}$

$\begin{gathered} \sf y = \frac{ \text- 5 + \sqrt{369} }{2} \end{gathered}$

$\begin{gathered} \sf y = \frac{ \text- 5 + 19}{2} \end{gathered}$

$\begin{gathered} \sf y = \frac{14}{2} \end{gathered}$

$\sf y = 7$

- Now, Mikay's age is 7 years old, Then substitute it to the first equation to find Kisses age.

$\begin{gathered} \begin{cases} \sf x = 7 + 5 \\ \sf y = 7 \end{cases} \end{gathered}$

$\begin{gathered} \begin{cases} \sf x = 12 \\ \sf y = 7 \end{cases} \end{gathered}$

- Therefore, the age of Kisses is, $\large \boxed{ \sf \green{ \: 12 \: yrs. \: old \: }}$ while Mikay's age is $\large \boxed{ \sf \green{ \: \: 7 \: yrs. \: old \: \: }}$

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