# 7.6E: Exercises

- Page ID
- 30947

**Rational Equation Number Applications**

In the following exercises, solve number applications

The sum of the reciprocals of two consecutive odd integers is \(−\dfrac{16}{63}\). Find the two numbers.

**Answer**-
−9, −7

The sum of the reciprocals of two consecutive odd integers is \(\dfrac{28}{195}\). Find the two numbers.

The sum of the reciprocals of two consecutive even integers is \(\dfrac{5}{12}\). Find the two numbers.

**Answer**-
4, 6

The sum of the reciprocals of two consecutive even integers is \(\dfrac{11}{60}\). Find the two numbers

The sum of the reciprocals of two consecutive integers is \(−\dfrac{19}{90}\). Find the two numbers.

**Answer**-
−10, −9

The sum of the reciprocals of two consecutive integers is \(\dfrac{19}{90}\). Find the two numbers.

The sum of a number and its reciprocal is \(\dfrac{5}{2}\). Find the number(s).

**Answer**-
2, \( \tfrac{1}{2} \)

The sum of a number and its reciprocal is \(\dfrac{41}{20}\). Find the number(s).

The sum of a number and twice its reciprocal is \(\dfrac{9}{2}\). Find the number(s).

**Answer**-
\(\dfrac{1}{2}\), 4

The sum of a number and twice its reciprocal is \(\dfrac{17}{6}\). Find the number(s).

The sum of the reciprocals of two numbers is \(\dfrac{15}{8}\), and the second number is 2 larger than the first. Find the two numbers.

**Answer**-
{\(\dfrac{2}{3}\), \(\dfrac{8}{3}\)} and {\(−\dfrac{8}{5}\), \(\dfrac{2}{5}\)}

The sum of the reciprocals of two numbers is \(\dfrac{16}{15}\), and the second number is 1 larger than the first. Find the two numbers.

When the same number is added to both the numerator and denominator of the fraction \(\dfrac{3}{7}\), the result is \(\dfrac{2}{3}\). What is the number?

**Answer**-
The number added is \(5\).

When the same number is added to both the numerator and denominator of the fraction \(\dfrac{5}{8}\), the result is \(\dfrac{3}{4}\). What is the number?

When the same number is added to both the numerator and denominator of the fraction \(\dfrac{3}{8}\), the result is \(\dfrac{1}{6}\). What is the number?

**Answer**-
The number added is \(−2\).

When the same number is added to both the numerator and denominator of the fraction \(\dfrac{7}{9}\), the result is \(\dfrac{2}{3}\). What is the number?

When the same number is subtracted to both the numerator and denominator of the fraction \(\dfrac{1}{10}\), the result is \(\dfrac{2}{3}\). What is the number?

**Answer**-
The number subtracted is \(−17\).

When the same number is subtracted to both the numerator and denominator of the fraction \(\dfrac{3}{4}\), the result is \(\dfrac{5}{6}\). What is the number?

When the same number is subtracted from both the numerator and denominator of the fraction \(\dfrac{7}{12}\), the result is \(\dfrac{1}{2}\). What is the number?

**Answer**-
\(2\)

When the same number is added to both the numerator and denominator of the fraction \(\dfrac{13}{15}\), the result is \(\dfrac{8}{9}\). What is the number?

One-third of a number added to the reciprocal of number yields \(\dfrac{13}{6}\). What is the number?

**Answer**-
\(x= \dfrac{1}{2}, 6\)

Four-fifths of a number added to the reciprocal of number yields \(\dfrac{81}{10}\). What is the number?

One-half of a number added to twice the reciprocal of the number yields \(2\). What is the number?

**Answer**-
\(2\)

One-fourth of a number added to four times the reciprocal of the number yields \(\dfrac{-10}{3}\). What is the number?