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6. solve each equation. write each solution as a fraction and as a deci…

| Equation | Solution (Fraction) | Solution (Decimal) | |----------|---------------------|--------------------| | $2x=3$ | $\frac{3}{2}$ | $1.5$ | | $5y=3$ | $\frac{3}{5}$ | $0.6$…

分類: algebra 更新時間: 2026-02-09

題目

  1. solve each equation. write each solution as a fraction and as a decimal

equation | solution (fraction) | solution (decimal)
$2x=3$
$5y=3$
$0.3z=0.09$

problems 7-10: each lap around a track is 400 meters. how many meters will someone run in:

  1. 2 laps?
  2. 5 laps?
  3. $x$ laps?
  4. if sol ran 7,600 meters, how many laps did they run? explain your thinking

解題步驟

  1. Understand the question
    1. solve each equation. write each solution as a fraction and as a decimal

    equation | solution (fraction) | solution (decimal)
    $2x=3$
    $5y=3$
    $0.3z=0.09$

    problems 7-10: each lap around a track is 400 meters. how many meters will someone run in:

    1. 2 laps?
    2. 5 laps?
    3. $x$ laps?
    4. if sol ran 7,600 meters, how many laps did they run? explain your thinking
  2. Response

    ---

    Problem 6
  3. Explanation

    Step1: Solve $2x=3$ for $x$

    Divide both sides by 2:
    $x=\frac{3}{2}$
    Convert to decimal: $x=1.5$

    Step2: Solve $5y=3$ for $y$

    Divide both sides by 5:
    $y=\frac{3}{5}$
    Convert to decimal: $y=0.6$

    Step3: Solve $0.3z=0.09$ for $z$

    Divide both sides by 0.3:
    $z=\frac{0.09}{0.3}=\frac{9}{30}=\frac{3}{10}$
    Convert to decimal: $z=0.3$

  4. Explanation

    Step1: 2 laps total distance

    Multiply laps by 400m:
    $2 \times 400 = 800$

    Step2: 5 laps total distance

    Multiply laps by 400m:
    $5 \times 400 = 2000$

    Step3: $x$ laps total distance

    Multiply laps by 400m:
    $x \times 400 = 400x$

    Step4: Find laps for 7600m

    Divide total meters by 400m:
    $\frac{7600}{400}=19$

  5. Final answer

    | Equation | Solution (Fraction) | Solution (Decimal) |
    |----------|---------------------|--------------------|
    | $2x=3$ | $\frac{3}{2}$ | $1.5$ |
    | $5y=3$ | $\frac{3}{5}$ | $0.6$ |
    | $0.3z=0.09$ | $\frac{3}{10}$ | $0.3$ |

    ---

    Problems 7-10

答案

Response

---

Problem 6

Explanation

Step1: Solve $2x=3$ for $x$

Divide both sides by 2:
$x=\frac{3}{2}$
Convert to decimal: $x=1.5$

Step2: Solve $5y=3$ for $y$

Divide both sides by 5:
$y=\frac{3}{5}$
Convert to decimal: $y=0.6$

Step3: Solve $0.3z=0.09$ for $z$

Divide both sides by 0.3:
$z=\frac{0.09}{0.3}=\frac{9}{30}=\frac{3}{10}$
Convert to decimal: $z=0.3$

Answer

| Equation | Solution (Fraction) | Solution (Decimal) |
|----------|---------------------|--------------------|
| $2x=3$ | $\frac{3}{2}$ | $1.5$ |
| $5y=3$ | $\frac{3}{5}$ | $0.6$ |
| $0.3z=0.09$ | $\frac{3}{10}$ | $0.3$ |

---

Problems 7-10

Explanation

Step1: 2 laps total distance

Multiply laps by 400m:
$2 \times 400 = 800$

Step2: 5 laps total distance

Multiply laps by 400m:
$5 \times 400 = 2000$

Step3: $x$ laps total distance

Multiply laps by 400m:
$x \times 400 = 400x$

Step4: Find laps for 7600m

Divide total meters by 400m:
$\frac{7600}{400}=19$

Answer

  1. 800 meters
  2. 2000 meters
  3. $400x$ meters
  4. 19 laps (Explanation: Each lap is 400 meters, so divide total distance 7600 by 400 to get the number of laps.)

Question Image

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Question Analysis

Subject mathematics
Sub Subject algebra
Education Level middle school
Difficulty unspecified
Question Type calculation
Multi Question No
Question Count 1
Analysis Status completed
Analyzed At 2026-02-09T10:10:12

OCR Text

Show OCR extraction
6. solve each equation. write each solution as a fraction and as a decimal
equation | solution (fraction) | solution (decimal)
$2x=3$
$5y=3$
$0.3z=0.09$

problems 7-10: each lap around a track is 400 meters. how many meters will someone run in:
7. 2 laps?
8. 5 laps?
9. $x$ laps?
10. if sol ran 7,600 meters, how many laps did they run? explain your thinking

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