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Popular >

Three numbers are in the ratio 1:3:7. if the sum of the three numbers is 320. what are the numbers?

Solution

Three numbers are in the ratio 1:3:7. if the sum of the three numbers is 320. what are the numbers?

Solution

The numbers : 29 \frac{1}{11}, 87 \frac{3}{11}, 203 \frac{7}{11}

Solution steps

Represent the numbers in ratio 1:3:7 with

x

x

3 x

7 x

Write an equation for the sum:

x + 3 x + 7 x = 320

Solve for

x, x + 3 x + 7 x = 320 : x = \frac{320}{11}

x = \frac{320}{11}

3 x = 3 \cdot \frac{320}{11} = \frac{960}{11}

7 x = 7 \cdot \frac{320}{11} = \frac{2240}{11}

Convert improper fractions to mixed numbers:

\frac{320}{11} = 29 \frac{1}{11}

Convert improper fractions to mixed numbers:

\frac{960}{11} = 87 \frac{3}{11}

Convert improper fractions to mixed numbers:

\frac{2240}{11} = 203 \frac{7}{11}

The numbers : 29 \frac{1}{11}, 87 \frac{3}{11}, 203 \frac{7}{11}

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