To solve the problem where a number exceeds its three-fifths by 22, let's define the unknown number as [tex]\( x \)[/tex].
1. According to the problem, the equation can be set up as:
[tex]\[
x = \frac{3}{5}x + 22
\][/tex]
2. To isolate [tex]\( x \)[/tex], subtract [tex]\(\frac{3}{5}x\)[/tex] from both sides of the equation:
[tex]\[
x - \frac{3}{5}x = 22
\][/tex]
3. Combine the terms on the left side. [tex]\( x \)[/tex] is the same as [tex]\(\frac{5}{5}x\)[/tex]:
[tex]\[
\frac{5}{5}x - \frac{3}{5}x = 22
\][/tex]
4. Subtract the fractions:
[tex]\[
\frac{2}{5}x = 22
\][/tex]
5. To solve for [tex]\( x \)[/tex], multiply both sides by the reciprocal of [tex]\(\frac{2}{5}\)[/tex], which is [tex]\(\frac{5}{2}\)[/tex]:
[tex]\[
x = 22 \times \frac{5}{2}
\][/tex]
6. Calculate the right side:
[tex]\[
x = 55
\][/tex]
Therefore, the number is [tex]\( 55 \)[/tex].
