The sum of three integers is 37. The sum of the first and second integers exceeds the third by 45. The third integer is 20 less than the first. Find the three integers.

Solution

Solution

The numbers : 11 \frac{2}{3}, 33 \frac{2}{3}, - 8 \frac{1}{3}

Solution steps

Represent the numbers with

x, y, z

number 1 : x

number 2 : y

number 3 : z

A.T.Q.:

x + y + z = 37

x + y = \frac{1}{3} + 45

z = x - 20

x + y + z = 37, x + y = \frac{1}{3} + 45, z = x - 20 : x = \frac{35}{3}, y = \frac{101}{3}, z = - \frac{25}{3}

Convert improper fractions to mixed numbers:

\frac{35}{3} = 11 \frac{2}{3}

Convert improper fractions to mixed numbers:

\frac{101}{3} = 33 \frac{2}{3}

Convert improper fractions to mixed numbers:

\frac{25}{3} = 8 \frac{1}{3}

The numbers : 11 \frac{2}{3}, 33 \frac{2}{3}, - 8 \frac{1}{3}

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