Question

Three consecutive integers are such that when taken in ascending order and multiplied by 3,5and 7 respectively, their sum is 244.find the integer

Answer 1

Answer:

let the integers be x,x+1,x+2

3(x)+5(x+1)+7(x+2)=244

3x+5x+5+7x+14=244

15x+19=244

15x=225

x=225/15

x=15

x+1=16

x+2=17

the consecutive numbers are 15,16,17

Answer 2

❍ Let the three integers be x, (x + 1), (x + 2) respectively.

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$\underline{\bigstar\;\boldsymbol{According\;to\;the\;Question:}}$

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• When the three consecutive integers are multipled by 3, 5 and 7, their sum is 244.

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Therefore,

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$:\implies\sf{3(x)+5(x+1)+7(x+2)=244}\\\\\\\\:\implies\sf{3x+5x+5+7x+14=244}\\\\\\\\:\implies\sf{15x+19=244}\\\\\\\\:\implies\sf{15x=244-19}\\\\\\\\:\implies\sf{15x=225}\\\\\\\\:\implies\sf{x=\cancel{\dfrac{225}{15}}}\\\\\\\\:\implies\underline{\boxed{\frak{\pink{x=15}}}}{\;\bigstar}$

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Hence,

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• First integer = x = 15
• Second integer = (x + 1) = (15 + 1) = 16
• Third integer = (x + 2) = (15 + 2) = 17

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$\therefore\;{\underline{\sf{Hence,\;the\;three\;consecutive\;integers\;are\;{\textsf{\textbf{15,\;16\;}}}and\:{\textsf{\textbf{17}}}}.}}$