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 (Writing solutions as fraction and decimal)

Equation 1: \( 2x = 3 \)

Step 1: Isolate \( x \)

To solve for \( x \), divide both sides of the equation by 2:
\( x=\frac{3}{2} \)

Step 2: Convert to decimal

\( \frac{3}{2}=1.5 \)

Equation 2: \( 5y = 3 \)

Step 1: Isolate \( y \)

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

Step 2: Convert to decimal

\( \frac{3}{5}=0.6 \)

Equation 3: \( 0.3z = 0.09 \)

Step 1: Isolate \( z \)

Divide both sides by \( 0.3 \):
\( z=\frac{0.09}{0.3} \)
Simplify the fraction (multiply numerator and denominator by 100 to eliminate decimals):
\( z=\frac{9}{30}=\frac{3}{10} \)

Step 2: Convert to decimal

\( \frac{3}{10}=0.3 \)

Problem 7: 2 laps

Step 1: Calculate total meters

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

Problem 8: 5 laps

Step 1: Calculate total meters

Multiply laps by meters per lap:
Total meters \( = 400 \times 5 = 2000 \) meters

Problem 9: \( x \) laps

Step 1: General formula

For \( x \) laps, total meters \( = 400 \times x = 400x \) meters

Problem 10: Sol ran 7,600 meters. How many laps?

Step 1: Define the relationship

Let \( n \) = number of laps. We know:
Total meters \( = 400 \times n \)

Step 2: Solve for \( n \)

Given total meters = 7,600, substitute:
\( 7600 = 400n \)
Divide both sides by 400:
\( n=\frac{7600}{400}=19 \)

Final Answers (Problem 6 Table)

Equation	Solution (Fraction)	Solution (Decimal)
\( 5y = 3 \)	\( \frac{3}{5} \)	\( 0.6 \)
\( 0.3z = 0.09 \)	\( \frac{3}{10} \)	\( 0.3 \)

Problem 7 Answer:

\( 800 \) meters

Problem 8 Answer:

\( 2000 \) meters

Problem 9 Answer:

\( 400x \) meters

Problem 10 Answer:

Sol ran \( \boldsymbol{19} \) laps. (Explanation: Since 1 lap = 400 meters, divide total meters (7,600) by meters per lap (400): \( \frac{7600}{400}=19 \).)

Answer:

Problem 6: Solve each equation (Writing solutions as fraction and decimal)

Equation 1: \( 2x = 3 \)

Step 1: Isolate \( x \)

To solve for \( x \), divide both sides of the equation by 2:
\( x=\frac{3}{2} \)

Step 2: Convert to decimal

\( \frac{3}{2}=1.5 \)

Equation 2: \( 5y = 3 \)

Step 1: Isolate \( y \)

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

Step 2: Convert to decimal

\( \frac{3}{5}=0.6 \)

Equation 3: \( 0.3z = 0.09 \)

Step 1: Isolate \( z \)

Divide both sides by \( 0.3 \):
\( z=\frac{0.09}{0.3} \)
Simplify the fraction (multiply numerator and denominator by 100 to eliminate decimals):
\( z=\frac{9}{30}=\frac{3}{10} \)

Step 2: Convert to decimal

\( \frac{3}{10}=0.3 \)

Problem 7: 2 laps

Step 1: Calculate total meters

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

Problem 8: 5 laps

Step 1: Calculate total meters

Multiply laps by meters per lap:
Total meters \( = 400 \times 5 = 2000 \) meters

Problem 9: \( x \) laps

Step 1: General formula

For \( x \) laps, total meters \( = 400 \times x = 400x \) meters

Problem 10: Sol ran 7,600 meters. How many laps?

Step 1: Define the relationship

Let \( n \) = number of laps. We know:
Total meters \( = 400 \times n \)

Step 2: Solve for \( n \)

Given total meters = 7,600, substitute:
\( 7600 = 400n \)
Divide both sides by 400:
\( n=\frac{7600}{400}=19 \)

Final Answers (Problem 6 Table)

Equation	Solution (Fraction)	Solution (Decimal)
\( 5y = 3 \)	\( \frac{3}{5} \)	\( 0.6 \)
\( 0.3z = 0.09 \)	\( \frac{3}{10} \)	\( 0.3 \)

Problem 7 Answer:

\( 800 \) meters

Problem 8 Answer:

\( 2000 \) meters

Problem 9 Answer:

\( 400x \) meters

Problem 10 Answer:

Sol ran \( \boldsymbol{19} \) laps. (Explanation: Since 1 lap = 400 meters, divide total meters (7,600) by meters per lap (400): \( \frac{7600}{400}=19 \).)