Problems Involving Equations

Worked Example 4.1.1:

What must be added to the positive difference between \( \scriptsize 4 \frac{3}{10} \: and \: 7 \frac{2}{5}\! \!\)to obtain 25?

Solution

Let the number be y

\( \scriptsize y \: + \: \left ( 7 \frac{2}{5}\: – \: 4 \frac{3}{10} \right) \scriptsize = 25 \)

\( \scriptsize y + \left (\normalsize \frac{37}{5}\: – \: \frac{43}{10} \right) \scriptsize = 25 \)

\( \scriptsize y \: + \: \normalsize \frac{\left(74 \: – \: 43 \right) }{10} \scriptsize = 25 \)

\( \scriptsize y \: + \: \normalsize \frac{31}{10} \scriptsize = 25 \)

Multiply both sides by 10

\( \scriptsize 10 \: \times \: y \:+ \:10 \: \times \: \normalsize \frac{31}{10} \scriptsize = 25 \: \times \: 10 \)

\(\scriptsize = 10y \: + \: 31 = 250 \)

\(\scriptsize 10y = 250\: – \: 31 \)

\(\scriptsize 10y = 219 \)

Divide both sides by 10

\( \frac{10y}{10} = \frac{219}{10} \)

\( \scriptsize y = 21.9 \: or \: 21 \frac{9}{10} \)

Worked Example 4.1.2:

The sum of three numbers is 30. The middle number is 5 less than the largest number, while the smallest number is one-third of the largest number. Find the three numbers.

Solution