8) 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:
Answers
Answer:
Answer:Three consecutive integers are 7,8 and 9
Solution:
Let the numbers are x, x+1 and x+2
(Since these are consecutive integers)
they are taken in increasing order and multiplied by 2,3 and 4 respectively
So x becomes 2x
(x+1) becomes 3(x+1)
(x+2) becomes 4(x+2)
they add up to 74,so ATQ
\begin{lgathered}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 \\ \\\end{lgathered}
2x+3(x+1)+4(x+2)=74
2x+3x+3+4x+8=74
9x+11=74
9x=74−11
9x=63
x=
9
63
x=7
So,
Integers are 7,8,9
Verification:
\begin{lgathered}2 \times 7 + 3 \times 8 + 4 \times 9 \\ \\ = > 14 + 24 + 36 \\ \\ = >7 4 \\ \\\end{lgathered}
2×7+3×8+4×9
=>14+24+36
=>74
Hence the calculate integers are correct.
Hope it helps you.
Step-by-step explanation:
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