Let’s solve each proportion step by step. We’ll use cross-multiplication to find the missing letter in each problem, then round to the nearest tenth (one decimal place) as instructed.
---
Problem 2:
\[
\frac{15}{6} = \frac{24}{b}
\]
Cross-multiply:
\[
15 \cdot b = 6 \cdot 24
\]
\[
15b = 144
\]
Divide both sides by 15:
\[
b = \frac{144}{15} = 9.6
\]
✔ b = 9.6
---
Problem 4:
\[
\frac{38}{3} = \frac{14}{d}
\]
Cross-multiply:
\[
38 \cdot d = 3 \cdot 14
\]
\[
38d = 42
\]
Divide both sides by 38:
\[
d = \frac{42}{38} ≈ 1.105... → \text{Round to tenths: } 1.1
\]
✔ d = 1.1
---
Problem 6:
\[
\frac{b}{22} = \frac{100}{15}
\]
Wait — this is labeled “b” again? But we already solved for b in problem 2. Looking at the grid, each row has a different letter. Let me check the image layout again mentally — actually, looking at the structure:
Row 2 → letter b
Row 4 → letter d
Row 6 → letter f
Row 8 → letter h
Row 10 → letter i
Row 12 → letter l
So Problem 6 should be solving for
f, not b. The variable name in the equation might be mislabeled in my reading — let’s re-read carefully.
Actually, in the original image description, it says:
> Solve each missing letter. Round your answers to the tenths place.
And the equations are:
2. 15/6 = 24/b → solve for b
4. 38/3 = 14/d → solve for d
6. b/22 = 100/15 → wait, that can’t be right — if we’re solving for f, maybe it’s a typo in how I read it?
Hold on — perhaps the left column letters (a, c, e, g, i, k) are just labels for rows, and the right column letters (b, d, f, h, j, l) are the variables to solve for.
Looking again:
The table likely looks like:
| Row | Equation | Answer Letter |
|-----|----------------------|---------------|
| 2 | 15/6 = 24/b | b |
| 4 | 38/3 = 14/d | d |
| 6 | ? /22 = 100/15 | f ← so probably it's "f/22 = 100/15"
Yes! That makes sense. So Problem 6 is:
\[
\frac{f}{22} = \frac{100}{15}
\]
Cross-multiply:
\[
f \cdot 15 = 22 \cdot 100
\]
\[
15f = 2200
\]
\[
f = \frac{2200}{15} ≈ 146.666... → \text{Round to tenths: } 146.7
\]
✔ f = 146.7
---
Problem 8:
\[
\frac{10}{21} = \frac{g}{5}
\]
Wait — again, according to the pattern, this should be solving for
h, not g. Probably the equation is:
\[
\frac{10}{21} = \frac{h}{5}
\]
Cross-multiply:
\[
10 \cdot 5 = 21 \cdot h
\]
\[
50 = 21h
\]
\[
h = \frac{50}{21} ≈ 2.3809... → \text{Round to tenths: } 2.4
\]
✔ h = 2.4
---
Problem 10:
\[
\frac{10}{49} = \frac{35}{i}
\]
Cross-multiply:
\[
10 \cdot i = 49 \cdot 35
\]
\[
10i = 1715
\]
\[
i = \frac{1715}{10} = 171.5
\]
✔ i = 171.5
---
Problem 12:
\[
\frac{8}{39} = \frac{l}{60}
\]
Cross-multiply:
\[
8 \cdot 60 = 39 \cdot l
\]
\[
480 = 39l
\]
\[
l = \frac{480}{39} ≈ 12.307... → \text{Round to tenths: } 12.3
\]
✔ l = 12.3
---
Now, let’s list all the answers with their corresponding letters:
- b = 9.6
- d = 1.1
- f = 146.7
- h = 2.4
- i = 171.5
- l = 12.3
These values will fill in the mystery picture grid based on which answer matches which cell — but since the question only asks to solve the proportions, we’ve done that.
Final Answer:
b = 9.6, d = 1.1, f = 146.7, h = 2.4, i = 171.5, l = 12.3
Parent Tip: Review the logic above to help your child master the concept of proportion puzzle worksheet.
