Let's solve each ratio problem step by step to find the value of
x that makes the ratios equivalent.
We use the concept of
proportions:
If $ a : b = c : x $, then $ \frac{a}{b} = \frac{c}{x} $, and we can cross-multiply:
$ a \cdot x = b \cdot c $ → $ x = \frac{b \cdot c}{a} $
---
1. $ 12 : 72 = 6 : x $
$$
\frac{12}{72} = \frac{6}{x} \Rightarrow x = \frac{72 \cdot 6}{12} = \frac{432}{12} = 36
$$
✔ x = 36
---
2. $ 24 : 20 = 6 : x $
$$
\frac{24}{20} = \frac{6}{x} \Rightarrow x = \frac{20 \cdot 6}{24} = \frac{120}{24} = 5
$$
✔ x = 5
---
3. $ 105 : 15 = 119 : x $
$$
\frac{105}{15} = \frac{119}{x} \Rightarrow x = \frac{15 \cdot 119}{105} = \frac{1785}{105} = 17
$$
✔ x = 17
---
4. $ 32 : 20 = 96 : x $
$$
\frac{32}{20} = \frac{96}{x} \Rightarrow x = \frac{20 \cdot 96}{32} = \frac{1920}{32} = 60
$$
✔ x = 60
---
5. $ 1.5 : 20 = 6 : x $
$$
\frac{1.5}{20} = \frac{6}{x} \Rightarrow x = \frac{20 \cdot 6}{1.5} = \frac{120}{1.5} = 80
$$
✔ x = 80
---
6. $ 16 : 20 = 6 : x $
$$
\frac{16}{20} = \frac{6}{x} \Rightarrow x = \frac{20 \cdot 6}{16} = \frac{120}{16} = 7.5
$$
✔ x = 7.5
---
7. $ 20 : 30 = 25 : x $
$$
\frac{20}{30} = \frac{25}{x} \Rightarrow x = \frac{30 \cdot 25}{20} = \frac{750}{20} = 37.5
$$
✔ x = 37.5
---
8. $ 32 : 128 = 3 : x $
$$
\frac{32}{128} = \frac{3}{x} \Rightarrow x = \frac{128 \cdot 3}{32} = \frac{384}{32} = 12
$$
✔ x = 12
---
9. $ 40 : 23 = 200 : x $
$$
\frac{40}{23} = \frac{200}{x} \Rightarrow x = \frac{23 \cdot 200}{40} = \frac{4600}{40} = 115
$$
✔ x = 115
---
10. $ 37 : 41 = 111 : x $
$$
\frac{37}{41} = \frac{111}{x} \Rightarrow x = \frac{41 \cdot 111}{37} = \frac{4551}{37} = 123
$$
✔ x = 123
---
11. $ 28 : 1.4 = x : 7 $
$$
\frac{28}{1.4} = \frac{x}{7} \Rightarrow x = \frac{28 \cdot 7}{1.4} = \frac{196}{1.4} = 140
$$
✔ x = 140
---
12. $ x : 35 = 18 : 30 $
$$
\frac{x}{35} = \frac{18}{30} \Rightarrow x = \frac{35 \cdot 18}{30} = \frac{630}{30} = 21
$$
✔ x = 21
---
13. $ 192 : 144 = 48 : x $
$$
\frac{192}{144} = \frac{48}{x} \Rightarrow x = \frac{144 \cdot 48}{192} = \frac{6912}{192} = 36
$$
✔ x = 36
---
14. $ 14 : 5 = x : 2.5 $
$$
\frac{14}{5} = \frac{x}{2.5} \Rightarrow x = \frac{14 \cdot 2.5}{5} = \frac{35}{5} = 7
$$
✔ x = 7
---
✔ Final Answers:
| Problem | Value of x |
|--------|------------|
| 1 | 36 |
| 2 | 5 |
| 3 | 17 |
| 4 | 60 |
| 5 | 80 |
| 6 | 7.5 |
| 7 | 37.5 |
| 8 | 12 |
| 9 | 115 |
| 10 | 123 |
| 11 | 140 |
| 12 | 21 |
| 13 | 36 |
| 14 | 7 |
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Let me know if you'd like this in a printable format or need explanations for any specific one!
Parent Tip: Review the logic above to help your child master the concept of value of x worksheet.
