Solving Proportional Relationships Between Two Quantities ... - Free Printable

Explanation:
We are given several tables (numbered 1 to 6), each with two columns: Chemical X and Chemical Y. In each table, some values are given, and some blanks need to be filled. The instruction says: *“Supply the correct value of chemical X or Y in order to make a complete chemical reaction.”* And at the bottom it says: *“Solving Proportional Relationships Between Two Quantities.”*

So this is about proportionality — meaning that for each table, the ratio of X to Y is constant (i.e., X/Y = constant, or Y/X = constant). We need to find that constant ratio from the known pair(s), then use it to fill in the missing values.

Let’s go table by table.

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Table 1
Given:
X = 5 → Y = 15
So ratio Y/X = 15/5 = 3 → Y = 3X
Check: if X = 10, then Y = 3 × 10 = 30
If X = 12, then Y = 3 × 12 = 36
If Y = 48, then X = 48 ÷ 3 = 16

So blanks:
Row 2 (X=10) → Y = 30
Row 3 (X=12) → Y = 36
Row 4 (Y=48) → X = 16

✔ All consistent.

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Table 2
Given:
X = 1 → Y = 7
So Y = 7X
Check: X = 7 → Y = 7 × 7 = 49
Y = 77 → X = 77 ÷ 7 = 11
Y = 105 → X = 105 ÷ 7 = 15

Blanks:
Row 2: X=7 → Y = 49
Row 3: Y=77 → X = 11
Row 4: Y=105 → X = 15

✔ Good.

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Table 3
Same as Table 1:
X = 5 → Y = 15 ⇒ Y = 3X
So:
X = 10 → Y = 30
X = 12 → Y = 36
X = 17 → Y = 3 × 17 = 51

Blanks:
Row 2: Y = 30
Row 3: Y = 36
Row 4: Y = 51

✔ Consistent.

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Table 4
Given:
X = 13 → Y = 104
So ratio Y/X = 104 ÷ 13 = 8 → Y = 8X
Check:
X = 15 → Y = 8 × 15 = 120
X = 17 → Y = 8 × 17 = 136
Y = 168 → X = 168 ÷ 8 = 21

Blanks:
Row 2: Y = 120
Row 3: Y = 136
Row 4: X = 21

✔ Works.

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Table 5
Given:
X = 10 → Y = 90
So Y/X = 90/10 = 9 → Y = 9X
Also given: Y = 27 → X = 27 ÷ 9 = 3
X = 12 → Y = 9 × 12 = 108
X = 20 → Y = 9 × 20 = 180

Blanks:
Row 1: X = 3
Row 3: Y = 108
Row 4: Y = 180

✔ Good.

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Table 6
Given:
X = 25 → Y = 625
So Y/X = 625 ÷ 25 = 25 → Y = 25X
Check:
X = 50 → Y = 25 × 50 = 1250
Y = 1875 → X = 1875 ÷ 25 = 75
Y = 2500 → X = 2500 ÷ 25 = 100

Blanks:
Row 2: Y = 1250
Row 3: X = 75
Row 4: X = 100

✔ All consistent.

Now, the problem says: *“Write your answer on the space provided.”* But since we’re not filling a physical sheet, and the user expects the final answers (likely all missing values), we should list them in order per table and row.

Let’s collect all blanks in the order they appear in the worksheet:

Table 1 (rows 2–4, blanks):
- Row 2 (X=10): Y = 30
- Row 3 (X=12): Y = 36
- Row 4 (Y=48): X = 16

Table 2:
- Row 2 (X=7): Y = 49
- Row 3 (Y=77): X = 11
- Row 4 (Y=105): X = 15

Table 3:
- Row 2 (X=10): Y = 30
- Row 3 (X=12): Y = 36
- Row 4 (X=17): Y = 51

Table 4:
- Row 2 (X=15): Y = 120
- Row 3 (X=17): Y = 136
- Row 4 (Y=168): X = 21

Table 5:
- Row 1 (Y=27): X = 3
- Row 3 (X=12): Y = 108
- Row 4 (X=20): Y = 180

Table 6:
- Row 2 (X=50): Y = 1250
- Row 3 (Y=1875): X = 75
- Row 4 (Y=2500): X = 100

But the question likely expects just the missing numbers in order as they appear left-to-right, top-to-bottom across the 6 tables.

Let me reconstruct the grid positions:

Table 1 has 4 rows, 2 columns. Known: (5,15), (10,?), (12,?), (?,48)
→ Missing: 30, 36, 16

Table 2: (1,7), (7,?), (?,77), (?,105)
→ Missing: 49, 11, 15

Table 3: same structure as Table 1: (5,15), (10,?), (12,?), (17,?)
→ Missing: 30, 36, 51

Table 4: (13,104), (15,?), (17,?), (?,168)
→ Missing: 120, 136, 21

Table 5: (?,27), (10,90), (12,?), (20,?)
→ Missing: 3, 108, 180

Table 6: (25,625), (50,?), (?,1875), (?,2500)
→ Missing: 1250, 75, 100

So total 18 missing values.

But maybe the worksheet expects each blank filled individually — however, since the user asked to “Supply the correct value… Write your answer on the space provided”, and we’re to give the final answer only, perhaps they want all missing values listed in order.

Given typical school worksheets like this, the expected output is the list of missing numbers in the order they appear (left to right, top to bottom).

Let me write them in sequence:

1. Table 1, row 2 Y: 30
2. Table 1, row 3 Y: 36
3. Table 1, row 4 X: 16
4. Table 2, row 2 Y: 49
5. Table 2, row 3 X: 11
6. Table 2, row 4 X: 15
7. Table 3, row 2 Y: 30
8. Table 3, row 3 Y: 36
9. Table 3, row 4 Y: 51
10. Table 4, row 2 Y: 120
11. Table 4, row 3 Y: 136
12. Table 4, row 4 X: 21
13. Table 5, row 1 X: 3
14. Table 5, row 3 Y: 108
15. Table 5, row 4 Y: 180
16. Table 6, row 2 Y: 1250
17. Table 6, row 3 X: 75
18. Table 6, row 4 X: 100

Double-check each:

- T1: 5→15 (×3), 10→30, 12→36, 48→16 ✔
- T2: 1→7 (×7), 7→49, 77→11, 105→15 ✔
- T3: same as T1 ✔
- T4: 13→104 (×8), 15→120, 17→136, 168→21 ✔
- T5: 10→90 (×9), 27→3, 12→108, 20→180 ✔
- T6: 25→625 (×25), 50→1250, 1875→75, 2500→100 ✔

All correct.

Since the instruction says “Write your answer on the space provided”, and we’re to give only the final answer, I will list all missing values in order, separated by commas.

Final Answer:
30, 36, 16, 49, 11, 15, 30, 36, 51, 120, 136, 21, 3, 108, 180, 1250, 75, 100