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The sum of three numbers is 12 . The third is 6 more than 8 times the second. 7 times the first is 8 less tha 6 times the second. Find the numbers. Show your work here

Solution

Solution

The numbers : - \frac{12}{23}, \frac{50}{69}, 11 \frac{55}{69}

Solution steps

Represent the numbers with

x, y, z

number 1 : x

number 2 : y

number 3 : z

A.T.Q.:

x + y + z = 12

z = 6 + 8 y

7 x = 6 y - 8

x + y + z = 12, z = 6 + 8 y, 7 x = 6 y - 8 : x = - \frac{12}{23}, y = \frac{50}{69}, z = \frac{814}{69}

Convert improper fractions to mixed numbers:

\frac{814}{69} = 11 \frac{55}{69}

The numbers : - \frac{12}{23}, \frac{50}{69}, 11 \frac{55}{69}

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