You've uploaded a text-based image containing 5 problems involving
direct variation. Since there's no actual image with visual content, I’ll solve each of the 5 problems step by step and explain the concept.
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📌 Key Concept: Direct Variation
When we say "
y varies directly as x", it means:
>
y = kx
where
k is the constant of proportionality (also called the constant of variation).
To solve these problems, we:
1. Use the given pair (x, y) to find
k.
2. Then use that
k to find the unknown value when another x or y is given.
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## 🔢 Problem 1:
> Suppose y varies directly as x, and y = 10 when x = 2. Find y when x = 6.
✔ Step 1: Find k
Given: y = 10, x = 2
Use y = kx → 10 = k·2 →
k = 5
✔ Step 2: Find y when x = 6
y = kx = 5·6 =
30
✔ Answer: y = 30
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## 🔢 Problem 2:
> Suppose y varies directly as x, and y = 24 when x = 3. Find x when y = 48.
✔ Step 1: Find k
y = kx → 24 = k·3 →
k = 8
✔ Step 2: Find x when y = 48
48 = 8·x → x = 48 / 8 =
6
✔ Answer: x = 6
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## 🔢 Problem 3:
> Suppose y varies directly as x, and y = 20 when x = 4. Find y when x = 10.
✔ Step 1: Find k
20 = k·4 →
k = 5
✔ Step 2: Find y when x = 10
y = 5·10 =
50
✔ Answer: y = 50
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## 🔢 Problem 4:
> Suppose x varies directly as t, and x = 7 when t = 2. Find x when t = 10.
*(Note: Here it’s x varying directly as t — same idea!)*
✔ Step 1: Find k
x = kt → 7 = k·2 →
k = 3.5
✔ Step 2: Find x when t = 10
x = 3.5·10 =
35
✔ Answer: x = 35
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## 🔢 Problem 5:
> Suppose y varies directly as x, and y = 8 when x = 2/3. Find y when x = 1.
✔ Step 1: Find k
y = kx → 8 = k·(2/3)
Multiply both sides by 3/2:
k = 8 · (3/2) =
12
✔ Step 2: Find y when x = 1
y = 12·1 =
12
✔ Answer: y = 12
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## 🧾 Final Answers:
1.
y = 30
2.
x = 6
3.
y = 50
4.
x = 35
5.
y = 12
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Parent Tip: Review the logic above to help your child master the concept of direct variation worksheet with answer key.
