Question

There are two figures. The sum of both figures is
99. If the first is 9 short of second. What is the second figure?

Answer 1

Let's define the two figures. Let the first figure be \( x \) and the second figure be \( y \).

According to the problem, we have the following two equations:

1. The sum of both figures is 99:
\[
x + y = 99
\]

2. The first figure is 9 short of the second:
\[
x = y - 9
\]

Now, we can substitute the expression for \( x \) from the second equation into the first equation:

\[
(y - 9) + y = 99
\]

Combining the \( y \) terms:

\[
2y - 9 = 99
\]

Now, add 9 to both sides:

\[
2y = 99 + 9
\]
\[
2y = 108
\]

Next, divide both sides by 2 to solve for \( y \):

\[
y = \frac{108}{2} = 54
\]

Thus, the second figure \( y \) is **54**.

To verify, we can find \( x \):

\[
x = y - 9 = 54 - 9 = 45
\]

Now, check the sum:

\[
x + y = 45 + 54 = 99
\]

Both conditions are satisfied. Therefore, the second figure is indeed \( \boxed{54} \).