Question

order of operatiohere is another type of cross-number puzzle. the provided, but certain numbers are missing. follo insert numbers in the spaces so that the solutiona$3 + 6 × □ = 21$$□ - □ + □ = □$$□ - □ + □ = 1$$10 ÷ 2 + □ = 15$

Explanation:

Step1: Solve top row (PEMDAS first)

Let the missing number be $x$.
$$3 + 6 \times x = 21$$
First, subtract 3 from both sides:
$$6 \times x = 21 - 3 = 18$$
Then divide by 6:
$$x = \frac{18}{6} = 3$$

Step2: Solve bottom row

Let the missing number be $y$.
$$10 \div 2 + y = 15$$
First calculate division:
$$5 + y = 15$$
Subtract 5 from both sides:
$$y = 15 - 5 = 10$$

Step3: Solve first column

Let the missing number be $a$.
$$3 \times a - 10 = 10$$
Add 10 to both sides:
$$3 \times a = 20$$
$$a = \frac{20}{3}$$

Step4: Solve third column

Let the missing number be $b$.
$$6 \times b \div 2 = 2$$
Simplify division first:
$$6 \times b = 2 \times 2 = 4$$
$$b = \frac{4}{6} = \frac{2}{3}$$

Step5: Solve fifth column

Let the missing number be $c$.
$$3 \times c + 10 = 10$$
Subtract 10 from both sides:
$$3 \times c = 0$$
$$c = 0$$

Step6: Solve second row result

$$10 - 2 - 15 = -7$$

Step7: Solve fourth row result

$$\frac{20}{3} - \frac{2}{3} + 0 = \frac{18}{3} = 6$$

Answer:

Filled puzzle grid (row by row):

1. $3, +, 6, \times, 3, =, 21$
2. $\times, \blacksquare, \times, \blacksquare, \times, \blacksquare, -$
3. $\frac{20}{3}, -, \frac{2}{3}, +, 0, =, -7$
4. $-, \blacksquare, +, \blacksquare, +, \blacksquare, +$
5. $6, -, 4, +, 1, =, 1$
6. $=, \blacksquare, =, \blacksquare, =, \blacksquare, =$
7. $10, \div, 2, +, 10, =, 15$