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Linear Equations in One Variable
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04/08/2021 11:07 am
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Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.
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04/08/2021 11:09 am
Let the three consecutive integers are x, x+1 and x+2.
According to the question,
2x + 3(x+1) + 4(x+2) = 74
⇒ 2x + 3x +3 + 4x + 8 = 74
⇒ 9x + 11 = 74
⇒ 9x = 74 – 11
⇒ 9x = 63
⇒ x = \(\frac{63}{9}\)
⇒ x = 7
Thus, the numbers are:
x = 7
x + 1 = 8
x + 2 = 9