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Popular Word Problems >

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

T h e s u m o f tw o n u mb ers i s 30. I f f o u r t im es t h e l a r g er n u mb er i s s u b t r a c t e d f ro m t h ree t im es t h e s ma ll er n u mb er, t h e res u lt i s 8. F in d t h e n u mb ers .

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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