Question

two numbers add up to 70. one third of the larger number is 10 more than one seventh of the smaller number. Find the numbers ​

Answer 1

A n s w e r

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G i v e n

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• Two numbers add up to 70

• One third of the larger number is 10 more than one seventh of the smaller number

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F i n d

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• The numbers

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S o l u t i o n

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• Let the larger number be 'a'

• Let the smaller number be 'b'

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Given that , the numbers add up to 70

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So ,

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: ➜ a + b = 70

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: ➜ a = 70 - b ⚊⚊⚊⚊ ⓵

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Also given that , One third of the larger number is 10 more than one seventh of the smaller number

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: ➜ $\sf \dfrac { 1 } { 3 } \times a = \dfrac { 1 } { 7 } \times b + 10$

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: ➜ $\sf \dfrac { 1 } { 3 } \times a = \dfrac { b + 70} { 7 }$

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: ➜ 7a = 3(b + 70)

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: ➜ 7a = 3b + 210 ⚊⚊⚊⚊ ⓶

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⟮ Putting a = 70 - b from ⓵ to ⓶ ⟯

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: ➜ 7(70 - b) = 3b + 210

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: ➜ 490 - 7b = 3b + 210

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: ➜ 7b + 3b = 490 - 210

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: ➜ 10b = 280

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: ➜ $\sf b = \dfrac { 280 } { 10 }$

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: ➜ b = 28 ⚊⚊⚊⚊ ⓷

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• Hence the smaller number is 28

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⟮ Putting b = 28 from ⓷ to ⓵ ⟯

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: ➜ a = 70 - b

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: ➜ a = 70 - 28

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: : ➨ a = 42

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• Hence the greater number is 42

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∴ The two numbers are 42 & 28