9th grade Convert rates and units in several steps worksheet

Convert rates and units in several steps

Grade 9 Math Worksheet

Circle the best answer.

1. 1.

   A ride costs C = 0.8m + 6 dollars for m miles. Pia rewrites it for k kilometers (1 mile = 1.6 km). Which equation is right?

   • C = 0.5k + 3.75
   • C = 0.8k + 6
   • C = 0.5k + 6
   • C = 1.28k + 6
2. 2.

   A bike rental costs R = 12h + 5 dollars for h hours. Bo rewrites it for t minutes. Which equation is right?

   • R = 12t + 5
   • R = 720t + 5
   • R = 0.2t + 5
   • R = 0.2t + 0.083
3. 3.

   A tank holds V = 400 - 25d liters after d days. Ren rewrites it for w weeks (7 days each). Which equation is right?

   • V = 57.1 - 25w
   • V = 400 - 3.6w
   • V = 400 - 25w
   • V = 400 - 175w

4. Read this first

   Use this

   Runner A table. Seconds: 5, 10. Feet: 30, 60. Runner B: d = 2.4t, with d in yards and t in seconds.

5. 4.

   Kira compares two runners. Who is faster? Runner A's table gives feet; Runner B's equation gives yards (1 yard = 3 feet).

   • They are equal: both runners keep a steady rate, so neither is faster.
   • Runner A: B runs just 0.8 feet per second, against A's 6 feet per second.
   • Runner A: A's 6 is greater than B's 2.4, so A runs faster.
   • Runner B: 2.4 yards per second is 7.2 feet per second, faster than A's 6.

6. Use this

   Plan A table. Months: 1, 3. Dollars: 30, 70. Plan B: C = 5.5w + 12, with C in dollars and w in weeks.

7. 5.

   Zee compares monthly rates (4 weeks per month). Plan A is a table; Plan B is an equation in weeks. Which plan costs less per month?

   • They cost the same per month: both plans grow steadily each month.
   • Plan B: B's 5.5 is less than A's 20, so B costs less per month.
   • Plan A: B costs 5.5 × 4 = $22 a month, more than A's $20.
   • Plan B: B costs just 5.5 ÷ 4 = $1.38 a month, less than A's $20.

8. Use this

   Hose A table. Hours: 2, 5. Liters: 180, 450. Hose B: V = 1.8m, with V in liters and m in minutes.

9. 6.

   Luz compares two hoses. Which fills faster? Hose A's table gives liters and hours; Hose B's equation gives liters and minutes.

   • They fill equally fast: both hoses give a steady flow, so neither is faster.
   • Hose A: A's 90 is greater than B's 1.8, so A fills faster than B.
   • Hose A: B fills just 0.03 liters per hour, against A's 90 liters per hour.
   • Hose B: 1.8 liters per minute is 108 liters per hour, more than A's 90.

10. Use this

    Charger A table. Hours: 1, 2. Percent: 25, 50. Charger B: P = 0.5m, with P in percent and m in minutes.

11. 7.

    Noah compares two chargers. Which charges faster? Charger A's table uses hours; Charger B's equation uses minutes.

    • Charger B: 0.5 percent per minute is 30 percent per hour, more than A's 25.
    • They charge equally fast: both chargers give a steady rate, so neither is faster.
    • Charger A: B charges just 0.008 percent per hour, against A's 25 percent per hour.
    • Charger A: A's 25 is greater than B's 0.5, so A charges faster than B.
12. 8.

    Esme compares gyms. Gym A: $12 a month plus a $30 signup fee. Gym B: $5 a week (4 weeks per month). After how many whole months is Gym A cheaper?

    • 3 months
    • 4 months
    • 1 month
    • Not at any point, because $5 is less than $12
13. 9.

    Ari compares streaming plans. Plan A: $9 a month plus a $24 setup fee. Plan B: $3 a week (4 weeks per month). After how many whole months is Plan A cheaper?

    • 9 months
    • 8 months
    • 2 months
    • Not at any point, because $3 is less than $9
14. 10.

    Jun compares phone plans. Plan A: $10 plus $0.004 per megabyte. Plan B: $5 per gigabyte (1 GB = 1,000 MB). After how many whole gigabytes is Plan A cheaper?

    • 11 GB
    • 1 GB
    • 10 GB
    • 3 GB