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the sum of six times a number and five times another number is 648. However the difference between two times the first number and five times the second number is 600. Determine the numbers.

Solution

Solution

The numbers : 156, - 57 \frac{3}{5}

Solution steps

Represent the numbers with

x and y

number 1 : x

number 2 : y

A.T.Q.:

6 x + 5 y = 648

2 x - 5 y = 600

6 x + 5 y = 648, 2 x - 5 y = 600 : x = 156, y = - \frac{288}{5}

Convert improper fractions to mixed numbers:

\frac{288}{5} = 57 \frac{3}{5}

The numbers : 156, - 57 \frac{3}{5}

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