Let’s solve each problem one by one. We’re finding unknown values in equivalent ratios — that means the two ratios are equal, like fractions.
We can think of a ratio like “a : b” as the fraction a/b. So if we have:
> 16 : 20 = x : 5
That means:
> 16/20 = x/5
Now let’s solve each one carefully.
---
1) 16 : 20 = x : 5
→ 16/20 = x/5
Simplify 16/20 → divide numerator and denominator by 4 → 4/5
So: 4/5 = x/5 → x = 4
✔
---
2) 78 : 169 = 12 : y
→ 78/169 = 12/y
Cross-multiply: 78 × y = 169 × 12
Calculate 169 × 12:
169 × 10 = 1690
169 × 2 = 338
Total = 1690 + 338 = 2028
So: 78y = 2028
Divide both sides by 78:
2028 ÷ 78 → Let’s do it step by step:
78 × 26 = ?
78 × 20 = 1560
78 × 6 = 468
1560 + 468 = 2028 → Yes!
So y = 26
✔
---
3) 8 : 60 = 4 : p
→ 8/60 = 4/p
Simplify 8/60 → divide by 4 → 2/15
So: 2/15 = 4/p
Cross-multiply: 2p = 15 × 4 = 60
p = 60 ÷ 2 = 30
✔
---
4) 40 : 16 = l : 22
→ 40/16 = l/22
Simplify 40/16 → divide by 8 → 5/2
So: 5/2 = l/22
Cross-multiply: 2l = 5 × 22 = 110
l = 110 ÷ 2 = 55
✔
---
5) 56 : 24 = 7 : z
→ 56/24 = 7/z
Simplify 56/24 → divide by 8 → 7/3
So: 7/3 = 7/z → z = 3
✔
---
6) q : 2 = 35 : 10
→ q/2 = 35/10
Simplify 35/10 → 7/2
So: q/2 = 7/2 → q = 7
✔
---
7) 21 : a = 3 : 4
→ 21/a = 3/4
Cross-multiply: 3a = 21 × 4 = 84
a = 84 ÷ 3 = 28
✔
---
8) 3 : c = 27 : 90
→ 3/c = 27/90
Simplify 27/90 → divide by 9 → 3/10
So: 3/c = 3/10 → c = 10
✔
---
9) 42 : 18 = 35 : d
→ 42/18 = 35/d
Simplify 42/18 → divide by 6 → 7/3
So: 7/3 = 35/d
Cross-multiply: 7d = 3 × 35 = 105
d = 105 ÷ 7 = 15
✔
---
10) 20 : 150 = s : 30
→ 20/150 = s/30
Simplify 20/150 → divide by 10 → 2/15
So: 2/15 = s/30
Cross-multiply: 15s = 2 × 30 = 60
s = 60 ÷ 15 = 4
✔
---
11) 48 : e = 20 : 25
→ 48/e = 20/25
Simplify 20/25 → 4/5
So: 48/e = 4/5
Cross-multiply: 4e = 48 × 5 = 240
e = 240 ÷ 4 = 60
✔
---
12) 4 : 11 = f : 44
→ 4/11 = f/44
Cross-multiply: 11f = 4 × 44 = 176
f = 176 ÷ 11 = 16
✔
---
13) e : 10 = 6 : 5
→ e/10 = 6/5
Cross-multiply: 5e = 6 × 10 = 60
e = 60 ÷ 5 = 12
✔
*(Note: This is a different “e” than #11 — just reuse of letter)*
---
14) 18 : j = 9 : 7
→ 18/j = 9/7
Cross-multiply: 9j = 18 × 7 = 126
j = 126 ÷ 9 = 14
✔
---
Final Answer:
1) x = 4
2) y = 26
3) p = 30
4) l = 55
5) z = 3
6) q = 7
7) a = 28
8) c = 10
9) d = 15
10) s = 4
11) e = 60
12) f = 16
13) e = 12
14) j = 14
Parent Tip: Review the logic above to help your child master the concept of ratios and equivalent ratios worksheet.
