Practice Questions Worksheet for Education and IQ Test [Answer is ... - Free Printable

Let's solve this step by step using the image and the given equations.

We are given three equations with symbols:

1. 🏀 + 🏀 + 🏀 = 18
2. 🏀 + ⚽ - 15 = 🏀🏀 (two basketballs)
3. ⚽ + ⚽ × 🏀½ = ?

We need to find the value of the third equation, where the basketball is half (only half of a basketball is shown).

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Step 1: Solve for the value of 🏀

From equation 1:
> 🏀 + 🏀 + 🏀 = 18
> 3 × 🏀 = 18
> 🏀 = 18 ÷ 3 = 6

So, basketball (🏀) = 6

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Step 2: Use equation 2 to find the value of ⚽

Equation 2:
> 🏀 + ⚽ - 15 = 🏀 + 🏀
> 6 + ⚽ - 15 = 6 + 6
> 6 + ⚽ - 15 = 12
> ⚽ - 9 = 12
> ⚽ = 12 + 9 = 21

So, soccer ball (⚽) = 21

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Step 3: Evaluate the third equation

> ⚽ + ⚽ × 🏀½ = ?

Note: The symbol 🏀½ means half a basketball, so its value is:
> ½ × 🏀 = ½ × 6 = 3

Now plug in the values:
> ⚽ + ⚽ × 🏀½
> = 21 + 21 × 3

But remember order of operations (PEMDAS): multiplication before addition.

> = 21 + (21 × 3)
> = 21 + 63
> = 84

Wait — but 84 is not among the options.

Options are:
A) 63
B) 90
C) 126
D) 252

Hmm... did we make a mistake?

Let’s double-check.

Wait — maybe the half basketball is not just half the value, but represents something else?

Alternatively, perhaps the half basketball is meant to be interpreted as a single unit, like a variable, or maybe it's a typo?

But logically, if 🏀 = 6, then half of it should be 3.

But let’s recheck equation 2 carefully.

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Re-examining Equation 2:

> 🏀 + ⚽ - 15 = 🏀🏀

The right side shows two basketballs — that's clearly 6 + 6 = 12

Left side:
6 + ⚽ - 15 = 12
→ ⚽ = 12 + 15 - 6 = 21 → correct.

So ⚽ = 21

Now equation 3:
> ⚽ + ⚽ × 🏀½ = ?

Is it possible the half basketball is not 3?

Wait — could the half basketball represent a different object? But it's clearly half of a basketball.

Maybe the expression is:

> ⚽ + ⚽ × (half basketball)

Which is:
21 + 21 × 3 = 21 + 63 = 84 → not an option.

But 84 isn't listed.

Wait — what if the operation order is misread?

Could it be:

> (⚽ + ⚽) × 🏀½ = ?

But no — the symbols are:
⚽ + ⚽ × 🏀½

So multiplication comes first.

Unless there's a different interpretation.

Wait — maybe the half basketball is actually a symbol representing half of a basketball, but in terms of value, it's 3, which seems correct.

But 84 isn’t an option.

Wait — could the half basketball be interpreted as a fraction of the full one, but maybe it's a variable?

No, it's clearly half.

Alternative idea: Maybe the half basketball is meant to represent a quarter? No — it's half.

Wait — look at the last equation again:

> ⚽ + ⚽ × 🏀½ = ?

But perhaps the half basketball is not a multiplier — but maybe it's a different kind of symbol?

Wait — maybe the half basketball is actually a basketball divided by 2, but maybe we're supposed to interpret it as value 6/2 = 3, which we did.

Still gives 84.

But 84 is not an option.

Wait — maybe I made a mistake in equation 2.

Let me write it again:

> 🏀 + ⚽ - 15 = 🏀 + 🏀

We know 🏀 = 6

So left: 6 + ⚽ - 15
Right: 6 + 6 = 12

So:
6 + ⚽ - 15 = 12
→ ⚽ - 9 = 12
→ ⚽ = 21 → correct.

Now equation 3: ⚽ + ⚽ × 🏀½

= 21 + 21 × 3 = 21 + 63 = 84 → not an option.

But wait — maybe the half basketball is not 3, but 6? That doesn’t make sense.

Or maybe the half basketball is a separate symbol?

Wait — perhaps the half basketball is not half of the value, but represents a different quantity?

But it's clearly half of a basketball.

Wait — could it be that the half basketball is a clue that the basketball is worth 6, so half is 3 — correct.

But 84 is not among the choices.

Let’s check the options:

A) 63
B) 90
C) 126
D) 252

Hmm.

What if the multiplication is not between ⚽ and 🏀½, but the entire expression is:

⚽ + ⚽ × 🏀½

But maybe it's (⚽ + ⚽) × 🏀½? But that would be written differently.

No — standard order applies.

Wait — another idea: Could the half basketball represent 6, but only because it's half of a full one, but maybe it's a trick?

No.

Wait — maybe the half basketball is a basketball, but only half is shown, so value is 3, but perhaps it's used in multiplication.

But 21 + 21 × 3 = 84.

Still not matching.

Wait — maybe the second equation has a typo in interpretation.

Let’s look again:

> 🏀 + ⚽ - 15 = 🏀🏀

Right side is two basketballs: 6 + 6 = 12

Left: 6 + ⚽ - 15 = 12 → ⚽ = 21 → correct.

Another idea: Maybe the half basketball is not 3, but 6, because it's still a basketball? But it's only half.

That doesn't make sense.

Wait — perhaps the half basketball is a new variable?

But no — it’s clearly half of a basketball.

Wait — maybe the half basketball is meant to be a basketball divided by 2, so value 3.

But then answer is 84.

But 84 is not an option.

Wait — unless I miscalculated.

Let’s try plugging in the answer choices and see which one fits.

Suppose the answer is C) 126

Then:
⚽ + ⚽ × 🏀½ = 126
21 + 21 × x = 126
21 × x = 105
x = 5

So half basketball = 5 → full basketball = 10

But from first equation: 3 × 🏀 = 18 → 🏀 = 6 → contradiction.

Try D) 252

21 + 21 × x = 252
21x = 231 → x = 11 → half basketball = 11 → full = 22 → contradicts 🏀 = 6

Try B) 90

21 + 21x = 90 → 21x = 69 → x ≈ 3.28 → not nice number

Try A) 63

21 + 21x = 63 → 21x = 42 → x = 2 → half basketball = 2 → full = 4

But first equation: 3×🏀 = 18 → 🏀 = 6 → contradiction.

So none work?

Wait — unless my assumption about the second equation is wrong.

Let’s re-express equation 2:

> 🏀 + ⚽ - 15 = 🏀🏀

But maybe the right side is not two basketballs, but a basketball and a half basketball?

Wait — no — it shows two full basketballs.

Look at the image:

In equation 2: the result is two full basketballs, side by side.

So it's 6 + 6 = 12

So equation 2: 6 + ⚽ - 15 = 12 → ⚽ = 21

Correct.

But then equation 3: 21 + 21 × 3 = 84 → not an option.

Wait — could the half basketball be a basketball with value 6, but only half is shown, so maybe it's 6, not 3?

But that would be inconsistent.

Wait — maybe the half basketball is a symbol for 6, but it's half, so value is 6?

That doesn’t make sense.

Wait — another possibility: Order of operations — is it possible that the expression is:

⚽ + ⚽ × 🏀½

But maybe it's intended to be:

(⚽ + ⚽) × 🏀½

Then: (21 + 21) × 3 = 42 × 3 = 126 → which is option C

Ah! That's interesting.

But why would it be grouped like that?

Because the image might have spacing that suggests grouping?

But in standard math notation, multiplication comes before addition.

However, sometimes in puzzles, the layout can suggest grouping.

Let’s look at the image:

It says:
⚽ + ⚽ × 🏀½ = ?

There’s no parentheses, so normally it’s 21 + (21 × 3) = 84

But if it were (⚽ + ⚽) × 🏀½ = 42 × 3 = 126 → option C

And 126 is an option.

Also, if we consider that the half basketball is 3, and the total is 126, it works.

But why would it be grouped?

Wait — maybe the half basketball is not 3, but 6, because it's a half, but represents the whole?

No.

Wait — another idea: Could the half basketball be a basketball divided by 2, but in value, it's 6, meaning the full one is 12?

But first equation: 3 × 🏀 = 18 → 🏀 = 6 → so full basketball is 6.

So half is 3.

But if we assume that the half basketball is 6, then full is 12, but that contradicts first equation.

So that can't be.

Wait — unless the first equation is not three full basketballs?

No — they are full.

Wait — perhaps the half basketball is a different object — like a "half" symbol, but value is 6?

No.

Wait — here's a breakthrough:

Maybe the half basketball is not half of a basketball, but a basketball divided by 2, so value is 3.

But then answer is 84.

But 84 is not an option.

But 126 is close.

Wait — what if the equation is:
⚽ + ⚽ × 🏀½ = ?

But if we interpret the half basketball as a basketball, i.e., value 6, even though it's half drawn?

But that would be inconsistent.

Wait — unless the half basketball is a basketball, and the drawing is just stylized.

But it's clearly half.

Wait — maybe the half basketball is a basketball, but only half is visible, so value is still 6.

Then:

⚽ + ⚽ × 🏀 = 21 + 21 × 6 = 21 + 126 = 147 → not an option.

No.

Wait — another idea: Maybe the half basketball is the value of a basketball divided by 2, so 3, but the multiplication is with the soccer ball?

No — it's ⚽ × 🏀½

Wait — perhaps the expression is:
⚽ + (⚽ × 🏀½)

Which is 21 + (21 × 3) = 84

Still not.

Wait — unless the answer is 63, and we made a mistake in soccer ball.

Let’s suppose the answer is 63.

Then:
⚽ + ⚽ × 🏀½ = 63
21 + 21 × x = 63 → 21x = 42 → x = 2 → so half basketball = 2 → full = 4

But from first equation: 3×🏀 = 18 → 🏀 = 6 → contradiction.

Similarly, 90: 21 + 21x = 90 → 21x = 69 → x = 3.28 → not integer.

126: 21 + 21x = 126 → 21x = 105 → x = 5 → half basketball = 5 → full = 10 → but first equation says 3×🏀 = 18 → 🏀 = 6 → contradiction.

252: 21 + 21x = 252 → 21x = 231 → x = 11 → half = 11 → full = 22 → contradiction.

So all give contradictions.

But wait — unless the first equation is not 3 basketballs = 18.

Let’s double-check.

First equation: 🏀 + 🏀 + 🏀 = 18 → 3×🏀 = 18 → 🏀 = 6 → correct.

Second equation: 🏀 + ⚽ - 15 = 🏀 + 🏀 → 6 + ⚽ - 15 = 12 → ⚽ = 21 → correct.

Third: ⚽ + ⚽ × 🏀½ = 21 + 21 × 3 = 84

But 84 not in options.

Wait — unless the half basketball is not 3, but 6, and the first equation is not three full ones?

No — they are full.

Wait — perhaps the half basketball is a basketball, and the drawing is misleading.

But it's clearly half.

Wait — another possibility: The half basketball is a symbol for 6, but it's half, so maybe it's 6, and the full one is 12?

But then first equation: 3×12 = 36 ≠ 18 → no.

So impossible.

Wait — unless the first equation is not three basketballs, but three half basketballs?

No — they are full.

Wait — maybe the half basketball in the third equation is a full basketball, but only half is shown.

But that doesn't help.

Wait — perhaps the operation is different.

Let’s look at the image again.

The third equation is:

⚽ + ⚽ × 🏀½ = ?

But maybe it's:

⚽ + ⚽ × (half basketball)

And half basketball = 3

So 21 + 21 × 3 = 84

But 84 not in options.

Unless the answer is 63, and we have a calculation error.

Wait — what if the second equation is:

🏀 + ⚽ - 15 = 🏀🏀

But the right side is two basketballs, so 6+6=12

Left: 6 + ⚽ - 15 = 12 → ⚽ = 21

Correct.

Perhaps the third equation is:

⚽ + ⚽ × 🏀½ = ?

But maybe the half basketball is a basketball, and the value is 6, but it's half, so maybe it's 6, and the full one is 6, so half is 3.

I'm stuck.

Wait — here's a new idea: Maybe the half basketball is not a value, but a symbol for division.

But no.

Wait — perhaps the half basketball is a basketball divided by 2, so it's 6/2 = 3, but in the context of the puzzle, it's used as a multiplier.

But still.

Wait — what if the expression is:
⚽ + ⚽ × 🏀½ = ?

But if we do: 21 + 21 × 3 = 84

But 84 is not an option.

But 84 is close to 63, 90, 126.

Wait — 126 is 21 × 6

21 × 6 = 126

And 6 is the value of a full basketball.

So if the half basketball was 6, then 21 × 6 = 126, plus 21 = 147

No.

Wait — what if the expression is:
⚽ + ⚽ × 🏀 = 21 + 21 × 6 = 21 + 126 = 147 → not an option.

No.

Wait — perhaps the half basketball is a basketball, and the drawing is just artistic.

But then value is 6.

But then 21 + 21 × 6 = 147 → not an option.

Wait — unless the multiplication is only on the soccer ball.

No.

Another idea: Maybe the half basketball is 6, but it's not multiplied, but added?

No.

Wait — let’s try to see if there’s a different interpretation of the second equation.

Equation 2: 🏀 + ⚽ - 15 = 🏀🏀

But maybe the right side is not two basketballs, but a basketball and a half basketball?

But the image shows two full basketballs.

Let’s assume it's two full ones.

So 12.

So 6 + ⚽ - 15 = 12 → ⚽ = 21

Correct.

Now, perhaps the third equation is:

⚽ + ⚽ × 🏀½ = ?

But if we do (⚽ + ⚽) × 🏀½ = (21 + 21) × 3 = 42 × 3 = 126

And 126 is option C.

And in many puzzles, the layout suggests grouping.

For example, if the symbols are close together, it might imply grouping.

But in this case, it's written as:

⚽ + ⚽ × 🏀½

With no parentheses.

But maybe the intention is that the multiplication is with the sum.

Alternatively, perhaps the half basketball is meant to be the value of a full basketball, but it's half, so maybe it's 6, and the full one is 6.

But then 21 + 21 × 6 = 147.

No.

Wait — another possibility: The half basketball is 6, but it's a half, so it's 6, and the full one is 12, but first equation says 3×12=36≠18

No.

Wait — unless the first equation is not three full basketballs, but three half basketballs.

But they are full.

Wait — look at the image: the first row has three full basketballs.

So 3×🏀 = 18 → 🏀 = 6

Second row: one full basketball, one soccer ball, minus 15, equals two full basketballs.

So 6 + ⚽ - 15 = 12 → ⚽ = 21

Third row: two soccer balls, times a half basketball.

So: ⚽ + ⚽ × 🏀½

= 21 + 21 × 3 = 84

But 84 not in options.

Unless the answer is 63, and we have a mistake.

Wait — what if the half basketball is a full basketball, and the value is 6, but the drawing is half, so it's 6.

Then 21 + 21 × 6 = 147

No.

Wait — perhaps the expression is:
⚽ + ⚽ × 🏀½ = ?

But maybe it's:
(⚽ + ⚽) × 🏀½ = (21 + 21) × 3 = 42 × 3 = 126

And 126 is option C.

And in many such puzzles, the grouping is implied by the layout.

For example, if the soccer balls are close together, and then multiplied by the half basketball.

So maybe the intended expression is:

(⚽ + ⚽) × 🏀½ = 126

So answer is C) 126

Even though mathematically, without parentheses, it should be 21 + (21 × 3) = 84, but since 84 is not an option, and 126 is, and it makes sense with the numbers, likely the intended answer is C) 126

Moreover, 126 is 21 × 6, and 6 is the value of a full basketball, but here it's half, so 3, but 42 × 3 = 126.

Yes.

So if the expression is grouped as (⚽ + ⚽) × 🏀½ = 42 × 3 = 126

Then answer is C) 126

Therefore, despite the order of operations, the puzzle likely intends for the addition to be done first.

So final answer: C) 126

\boxed{C}