Chapter 1.7, Problem 2P

To determine

To find: The age of the gym and auditorium buildings.

Answer to Problem 2P

The gym building is 7 years old and auditorium building is 28 years old.

Explanation of Solution

Given information: The gym is 21 years newer than the auditorium. The gym is also one fourth as old as the auditorium.

Calculation:

Let the age of auditorium as $a$ .

So, the age of

  $gym=a-21$ -----(1)

Because gym is 21 years newer means it has been build after 21 years than the auditorium built.

And gym is also ${\frac{1}{4}}^{th}$ as old as auditorium. Equation form of this is

  $gym=\frac{1}{4}a$ --------(2)

Solve the equations using substitution method,

Substitute $gym$ as $a-21$ into second equation.

  $\frac{1}{4}a=a-21$

Solve the equation for $a$ .

Multiply both sides of the equation by 4.

  $a=4a-84$

Subtract both sides 4a,

  $-3a=-84$

Divide both sides by -3.

  $a=28$

Plug in ‘ $a$ ’ as 28 into any of the equations to find age of gym,

  $\begin{array}{l}gym=28-21\\ gym=7\end{array}$

Conclusion: gym building is 7 years old and auditorium building is 28 years old.