Math Problem Statement

The attendant at a parking lot compared the number of hybrid vehicles to the total number of vehicles in the lot over a weekend. The ratios for the three days were equivalent. Complete the table. Day Hybrids Total Fri. 3 8 Sat. 56 Sun. 27 Question content area bottom Part 1 Day Hybrids Total Fri. 3 8 Sat.

enter your response here 56

Solution

The problem involves ratios that are equivalent across the three days. The ratio of hybrid vehicles to the total number of vehicles on Friday is given as:

Hybrids on FridayTotal on Friday=38\frac{\text{Hybrids on Friday}}{\text{Total on Friday}} = \frac{3}{8}

Since the ratios for all days are equivalent, the ratio for Saturday and Sunday must also equal 38\frac{3}{8}.

Saturday

You are provided the total number of vehicles on Saturday as 56. To find the number of hybrid vehicles on Saturday, we can set up a proportion:

38=Hybrids on Saturday56\frac{3}{8} = \frac{\text{Hybrids on Saturday}}{56}

Now, solve for the number of hybrids:

Hybrids on Saturday=38×56=21\text{Hybrids on Saturday} = \frac{3}{8} \times 56 = 21

Thus, the number of hybrids on Saturday is 21.

Sunday

For Sunday, the number of hybrid vehicles is provided as 27. To find the total number of vehicles, we again set up a proportion:

38=27Total on Sunday\frac{3}{8} = \frac{27}{\text{Total on Sunday}}

Now solve for the total:

Total on Sunday=8×273=72\text{Total on Sunday} = \frac{8 \times 27}{3} = 72

Thus, the total number of vehicles on Sunday is 72.

Completed Table:

DayHybridsTotal
Fri.38
Sat.2156
Sun.2772

Would you like further details or have any questions about this problem?

Related Questions:

  1. If the ratio had been 4:9, what would the table look like?
  2. How would you calculate the total number of vehicles if only the hybrids were known for all three days?
  3. Can you explain why ratios are helpful in problems like this?
  4. What is the total number of hybrid vehicles over the weekend?
  5. If the ratio was changed on Sunday to 1:3, what would be the total?

Tip: When dealing with equivalent ratios, setting up proportions is a reliable way to find unknown values.

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Math Problem Analysis

Mathematical Concepts

Ratios
Proportions
Algebra

Formulas

Ratio formula: hybrids / total vehicles
Proportion formula: (hybrids on day 1 / total on day 1) = (hybrids on day 2 / total on day 2)

Theorems

Proportion Theorem

Suitable Grade Level

Grades 6-8