Question

spiral review

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

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

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.

Explanation:

Problem 6: Solve each equation, write solution as fraction and decimal

Equation \( 2x = 3 \)

Step 1: Isolate \( x \)

Divide both sides by 2: \( x = \frac{3}{2} \)

Step 2: Convert to decimal

\( \frac{3}{2} = 1.5 \)
Solution (Fraction): \( \frac{3}{2} \); Solution (Decimal): \( 1.5 \)

Equation \( 5y = 3 \)

Step 1: Isolate \( y \)

Divide both sides by 5: \( y = \frac{3}{5} \)

Step 2: Convert to decimal

\( \frac{3}{5} = 0.6 \)
Solution (Fraction): \( \frac{3}{5} \); Solution (Decimal): \( 0.6 \)

Equation \( 0.3z = 0.09 \)

Step 1: Isolate \( z \)

Divide both sides by 0.3: \( z = \frac{0.09}{0.3} = \frac{9}{30} = \frac{3}{10} \) (simplified fraction)

Step 2: Convert to decimal

\( \frac{3}{10} = 0.3 \)
Solution (Fraction): \( \frac{3}{10} \); Solution (Decimal): \( 0.3 \)

Problem 7: 2 laps

Step 1: Calculate total meters

Each lap is 400 meters, so for 2 laps: \( 400 \times 2 = 800 \) meters

Total meters is 7600, each lap is 400 meters. To find laps, divide total meters by meters per lap: \( \frac{7600}{400} = 19 \). So Sol ran 19 laps.

Answer:

800 meters

Problem 8: 5 laps

Step 1: Calculate total meters

Each lap is 400 meters, so for 5 laps: \( 400 \times 5 = 2000 \) meters