Question

spiral review

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

equation\tsolution (fraction)\tsolution (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?\t8. 5 laps?\t9. x laps?
2. if sol ran 7,600 meters, how many laps did they run? explain your thinking.

Explanation:

Problem 6 (Solving Equations)

For \( 2x = 3 \)

Step1: Isolate \( x \) by dividing both sides by 2

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

Step2: Convert fraction to decimal

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

For \( 5y = 3 \)

Step1: Isolate \( y \) by dividing both sides by 5

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

Step2: Convert fraction to decimal

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

For \( 0.3z=0.09 \)

Step1: Isolate \( z \) by dividing both sides by 0.3

\( z=\frac{0.09}{0.3}=\frac{9}{30}=\frac{3}{10} \) (simplifying the fraction)

Step2: Convert fraction to decimal

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

Problem 7 (2 laps)

Step1: Multiply laps by meters per lap

Total meters \( = 2\times400 \)

Step2: Calculate the product

\( 2\times400 = 800 \)

(Problem 10):
We know each lap is 400 meters. Let the number of laps be \( n \). The total distance (7600 meters) is equal to the number of laps times 400 meters per lap (\( 400n = 7600 \)). To find \( n \), we divide the total distance by the distance per lap (\( \frac{7600}{400} \)) which gives 19.

Answer:

(Problem 7): 800 meters

Problem 8 (5 laps)

Step1: Multiply laps by meters per lap

Total meters \( = 5\times400 \)

Step2: Calculate the product

\( 5\times400=2000 \)