What does a duck do when it flies upside down? The answer to this… - Vidyadip

Question

What does a duck do when it flies upside down? The answer to this riddle is hidden in the equation given below: If $i + 69 = 70$, then $i = ?$ If $8u = 6u + 8$, then $u = ?$ If $4a = –5a + 45$, then $a = ?$ if $4q + 5 = 17$, then $q = ?$ If $- 5t - 60 = -70$, then $t = ?$ If $\frac{1}{4}\text{s} + 98 = 100$, then $s = ?$ If $\frac{5}{3}\text{p} + 9 = 24$, then = ______? If $3c = c + 12$, then $c =$ ______? If $3(k + 1) = 24$, then k = ______? For riddle answer: substitute the number for the letter it equals.

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Answer

We have, $i + 69 = 70$ [transposing $69$ to $RHS]$
$\Rightarrow i = 1$ and $8u = 6u + 8$
$\Rightarrow8\text{u}=6\text{u}+8$ [transposing $6u$ to $RHS]$
$\Rightarrow2\text{u}=8$
$\Rightarrow\frac{2\text{u}}{2}=\frac{8}{2}$ [dividing both sides by $2]$
$\Rightarrow\text{u}=4$
We have, $4a = -5a + 45$
$\Rightarrow4\text{a}+5\text{a}=45$ [transposing $(-5a)$ to $LHS]$
$\Rightarrow9\text{a}=45$
$\Rightarrow\frac{9\text{a}}{9}=\frac{45}{9}$ [dividing both sides by $9]$
$\Rightarrow\text{a}=5$ and $4q + 5 = 17$
$\Rightarrow4\text{q}=17-5$ [transposing $5$ to $RHS] $
$\Rightarrow4\text{q}=12$
$\Rightarrow\frac{4\text{q}}{4}=\frac{12}{4}$ [dividing both sides by $4]$
$\Rightarrow\text{q}=3$
We have,$ -5t - 60 = -70$
$\Rightarrow-5\text{t}=-70+60$ [transposing $(-60)$ to $RHS$]
$\Rightarrow-5\text{t}=-10$
$\Rightarrow\frac{-5\text{t}}{-5\text{}}=\frac{-10}{-5}$ [dividing both sides by $(-5)]$
$\Rightarrow\text{t}=2$ and $\frac{1}{4}\text{s}+98=100$
$\Rightarrow\frac{1}{4}\text{s}=100-98$ [transposing $98$ to $RHS]$
$\Rightarrow\frac{1}{4}\text{x}=2$
$\Rightarrow\frac{4}{4}\text{s}=4\times2$ [multiplying both sides by $4]$
$\Rightarrow\text{s}=8$
We have, $\frac{5}{3}\text{p}+9=24$
$\Rightarrow\frac{5}{3}\text{p}=24-9$ [transposing $9$ to $RHS]$
$\Rightarrow\frac{5}{3}\text{p}=15$
$\Rightarrow\frac{3}{5}\times\frac{5}{3}\text{p}=\frac{3}{5}\times15$
$\big[$ multiplying both sides by $\frac{3}{5}\big]$
$\Rightarrow\text{p}=9$
We have, $3c - c = 12$
$\Rightarrow3\text{c}=\text{c}+12$ [transposing c to $LHS]$
$\Rightarrow2\text{c}=12$
$\Rightarrow\frac{2\text{c}}{2}=\frac{12}{2}$ [dividing both sides by $2]$
We have, $3(k + 1) = 24$
$\Rightarrow\frac{3(\text{k}+1)=24}{3}=\frac{24}{3}$ [dividing both sides by $3]$
$\Rightarrow\text{k}+1=8$
$\Rightarrow\text{k}=8-1$ [transposing $1$ to $RHS]$
$\Rightarrow\text{k}=7$ By substituting the number for the letter it equals, we get

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