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Liono4ka [1.6K]
3 years ago
10

Seven times the difference of some number and 1 amounts to the quotient of 168 and 12

Mathematics
1 answer:
rjkz [21]3 years ago
5 0

Answer:

7 (x - 1) = 14

gives:   x = 3

Step-by-step explanation:

Let the number be x

According to Given conditions:

  • Difference of some number and 1 = x - 1
  • Seven times the difference of some number and 1 = 7 (x - 1)
  • Quotient of 168 and 12 = 168/12 = 14

According to given scenario:

7 (x - 1) = 14

Dividing both sides by 7

(x - 1) =2

Adding 1 on both sides:

x -1 +1 = 2 + 1

x = 3

I hope it will help you!

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\begin{array}{lrcll}(1) & 8x + 13y +7 & = & 180 & \\(2)& 9x - 7 + 13y +7 & = & 180 & \\(3)& 8x + 5y - 11 + z & = & 180 &\text{We can rearrange these to get:}\\(4)& 8x + 13y & = & 173 &\\(5) & 9x + 13y & = & 180 & \\(6)& 8x + 5y + z & = & 169 & \\(7)& x & = & \mathbf{7} & \text{Subtracted (4) from (5)} \\\end{array}

\begin{array}{lrcll}& 8(7) + 13y & = & 173 & \text{Substituted (7) into (4)} \\& 56 + 13y & = & 173 & \text{Simplified} \\& 13y & = & 117 & \text{Subtracted 56 from each side} \\(8)& y & =& \mathbf{9}&\text{Divided each side by 13}\\& 8(7) + 5(9) + z & = & 169 & \text{Substituted (8) and (7) into (6)} \\& 56 + 45 + z& = & 169 & \text{Simplified} \\& 101 + z& = & 169 & \text{Simplified} \\&z& = & \mathbf{68} & \text{Subtracted 101 from each side}\\\end{array}

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