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Popular Word Problems >

The sum of two numbers is 78. Five times the smaller number is 12 less than twice the larger number. What are the numbers?

Solution

T h e s u m o f tw o n u mb ers i s 78. F i v e t im es t h e s ma ll er n u mb er i s 12 l ess t han tw i ce t h e l a r g er n u mb er . Wha t a re t h e n u mb ers ?

Solution

The numbers : 20 \frac{4}{7}, 57 \frac{3}{7}

Solution steps

Represent the numbers with

x and y

:

number 1 : x

number 2 : y

A.T.Q.:

x + y = 78

5 x = 2 y - 12

x + y = 78, 5 x = 2 y - 12 : x = \frac{144}{7}, y = \frac{402}{7}

Convert improper fractions to mixed numbers:

\frac{144}{7} = 20 \frac{4}{7}

Convert improper fractions to mixed numbers:

\frac{402}{7} = 57 \frac{3}{7}

The numbers : 20 \frac{4}{7}, 57 \frac{3}{7}

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