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The sum of two numbers is 30. If four times the larger number is subtracted from three times the smaller number, the result is 8. Find the numbers.

Solution

The sum of two numbers is 30. If four times the larger number is subtracted from three times the smaller number, the result is 8. Find the numbers.

Solution

The numbers : 11 \frac{5}{7}, 18 \frac{2}{7}

Solution steps

Represent the numbers with

x and y

:

number 1 : x

number 2 : y

A.T.Q.:

x + y = 30

3 y - 4 x = 8

x + y = 30, 3 y - 4 x = 8 : x = \frac{82}{7}, y = \frac{128}{7}

Convert improper fractions to mixed numbers:

\frac{82}{7} = 11 \frac{5}{7}

Convert improper fractions to mixed numbers:

\frac{128}{7} = 18 \frac{2}{7}

The numbers : 11 \frac{5}{7}, 18 \frac{2}{7}

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