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Popular Word Problems >

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

t h e s u m o f s i x t im es a n u mb er an d f i v e t im es an o t h er n u mb er i s 648. Ho w e v er t h e d i ff ere n ce b e tw ee n tw o t im es t h e f i rs t n u mb er an d f i v e t im es t h e seco n d n u mb er i s 600. De t er min e t h e n u mb ers .

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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