Question

valentine’s day puzzle: integer multiplication and division find the value of each symbol. each symbol has the same value across equations. 1.
· 3 = -21 2.
÷ (-2) = -28 3. 98 =
·
4.
=
÷
5.
÷
·
=
6.
÷
=
÷
write the value of each symbol.
=
=
=
=
=
=

Explanation:

Step1: Solve for gift box

Let $g$ = gift box.
$\frac{g \cdot 3}{3} = \frac{-21}{3}$
$g = -7$

Step2: Solve for flower pot

Let $f$ = flower pot.
$f \div (-2) \cdot (-2) = -28 \cdot (-2)$
$f = 56$

Step3: Solve for heart with arrow

Let $h$ = heart with arrow.
$\frac{98}{g} = \frac{h \cdot g}{g}$
$\frac{98}{-7} = h$
$h = -14$

Step4: Solve for small heart

Let $s$ = small heart.
$g = \frac{f}{s}$
$s = \frac{f}{g}$
$s = \frac{56}{-7}$
$s = -8$

Step5: Solve for mug

Let $m$ = mug.
$\frac{m}{s} \cdot g = h$
$m = \frac{h \cdot s}{g}$
$m = \frac{-14 \cdot (-8)}{-7}$
$m = \frac{112}{-7}$
$m = -16$ Correction:
$\frac{m}{s} \cdot g = h$
$m = \frac{h \cdot s}{g}$
$m = \frac{-14 \cdot (-8)}{-7} = \frac{112}{-7} = -16$ Error fixed:
$\frac{m}{s} \cdot g = h$
$m = \frac{h \cdot s}{g} = \frac{(-14) \cdot (-8)}{-7} = \frac{112}{-7} = -16$ Recheck Step5:
$\frac{m}{s} \cdot g = h$
$\frac{m}{-8} \cdot (-7) = -14$
$m \cdot \frac{7}{8} = -14$
$m = -14 \cdot \frac{8}{7} = -16$ Correct

Step6: Solve for candy

Let $c$ = candy.
$\frac{f}{h} = \frac{c}{m}$
$c = \frac{f \cdot m}{h}$
$c = \frac{56 \cdot (-16)}{-14}$
$c = \frac{-896}{-14}$
$c = 64$ Correction Step4:
$g = f \div s$
$-7 = 56 \div s$
$s = 56 \div (-7) = -8$ Correct

Step5 recheck:
$\frac{m}{s} \cdot g = h$
$\frac{m}{-8} \cdot (-7) = -14$
$\frac{7m}{8} = -14$
$7m = -112$
$m = -16$ Correct

Step6:
$\frac{f}{h} = \frac{c}{m}$
$\frac{56}{-14} = \frac{c}{-16}$
$-4 = \frac{c}{-16}$
$c = (-4) \cdot (-16) = 64$ Correct

Final Corrected Answer:
Gift box = $-7$, Flower pot = $56$, Heart with arrow = $-14$, Small heart = $-8$, Mug = $-16$, Candy = $64$

(Corrected):

Step1: Solve for gift box

Let $g$ = gift box.
$g = \frac{-21}{3} = -7$

Step2: Solve for flower pot

Let $f$ = flower pot.
$f = -28 \times (-2) = 56$

Step3: Solve for heart with arrow

Let $h$ = heart with arrow.
$h = \frac{98}{g} = \frac{98}{-7} = -14$

Step4: Solve for small heart

Let $s$ = small heart.
$s = \frac{f}{g} = \frac{56}{-7} = -8$

Step5: Solve for mug

Let $m$ = mug.
$\frac{m}{s} \times g = h$
$m = \frac{h \times s}{g} = \frac{-14 \times (-8)}{-7} = -16$

Step6: Solve for candy

Let $c$ = candy.
$\frac{f}{h} = \frac{c}{m}$
$c = \frac{f \times m}{h} = \frac{56 \times (-16)}{-14} = 64$

Final Answer:

Gift box = $\boldsymbol{-7}$, Flower pot = $\boldsymbol{56}$, Heart with arrow = $\boldsymbol{-14}$, Small heart = $\boldsymbol{-8}$, Mug = $\boldsymbol{-16}$, Candy = $\boldsymbol{64}$

Answer:

Gift box = $-7$, Flower pot = $56$, Heart with arrow = $-14$, Small heart = $-8$, Mug = $2$, Candy = $-8$