Calculate the Exact Number of Parks with 24 Trees Planted

Q: Why do we need to find the total number of parks first?

The average formula requires knowing the total. Since average = total trees ÷ total parks, we need both values. We use the fact that total parks = known parks + unknown parks.

Q: How do I know which variable to solve for?

The question asks "How many parks planted 24 trees?" Let x represent this unknown quantity. Then build your equation around finding x.

Q: What does the average of 24.2 trees actually mean?

It means if you add up all trees from all parks and divide by the number of parks, you get 24.2. This is the key relationship that lets us set up our equation.

Q: Why do we get a decimal coefficient like 0.2x?

When we expand $ 24.2(5 + x) $, we get $ 121 + 24.2x $. The decimal comes from the average value 24.2, and that's perfectly normal in these problems.

Step-by-step video solution

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Step-by-step written solution

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1

Understand the problem

In each park of a city $24.2$ trees are planted on average.

In the first two parks, 19 trees are planted, while in the next three parks 28 are planted.

How many parks planted 24 trees?

2

Step-by-step solution

To solve this problem, let's calculate step by step:

Determine the total number of parks: Since all parks combined plant an average of 24.2 trees each, let's assume there are $n$ parks. This implies a total of $24.2n$ trees.
Calculate trees in known parks: The first two parks have 19 trees each, thus total $2 \times 19 = 38$ trees. The next three parks have 28 trees each, amounting to $3 \times 28 = 84$ trees. Together, they plant $38 + 84 = 122$ trees.
Set up the equation: Let $x$ be the number of parks that planted 24 trees. Then the rest of the parks account for $24x$ trees. Our equation becomes:

24.2n = 122 + 24x

Express $n$ in terms of $x$ :
Since $n = 2 + 3 + x$ (two parks with 19 trees, three with 28, and the ones we are solving for), we substitute this into the equation:

24.2(2 + 3 + x) = 122 + 24x

.

Solve for $x$ :

24.2 \times 5 + 24.2x = 122 + 24x

121 + 24.2x = 122 + 24x

121 + 24.2x - 24x = 122

0.2x + 121 = 122

0.2x = 1

x = \frac{1}{0.2} = 5

Therefore, $\boxed{5}$ parks planted exactly 24 trees. This confirms with answer choice (3).

3

Final Answer

$5$ parks

Key Points to Remember

Essential concepts to master this topic

Setup: Express total trees as sum of all individual parks
Technique: Use n = 5 + x to relate total parks to unknowns
Check: Verify average: (38 + 84 + 120)/10 = 242/10 = 24.2 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to include all parks in the total count
Don't set up n = x (only counting unknown parks) = wrong total! This ignores the 5 known parks and breaks the average calculation. Always count ALL parks: n = 2 + 3 + x for the complete system.

Practice Quiz

Test your knowledge with interactive questions

Norbert buys some new clothes.

When he gets home, he decides to work out how much each outfit cost him on average.

What answer should he come up with?

FAQ

Everything you need to know about this question

Why do we need to find the total number of parks first?

+

The average formula requires knowing the total. Since average = total trees ÷ total parks, we need both values. We use the fact that total parks = known parks + unknown parks.

How do I know which variable to solve for?

+

The question asks "How many parks planted 24 trees?" Let x represent this unknown quantity. Then build your equation around finding x.

What does the average of 24.2 trees actually mean?

+

It means if you add up all trees from all parks and divide by the number of parks, you get 24.2. This is the key relationship that lets us set up our equation.

Why do we get a decimal coefficient like 0.2x?

+

When we expand $24.2(5 + x)$ , we get $121 + 24.2x$ . The decimal comes from the average value 24.2, and that's perfectly normal in these problems.

How can I check if x = 5 is really correct?

+

Calculate the total: 2 parks × 19 + 3 parks × 28 + 5 parks × 24 = 38 + 84 + 120 = 242 trees. Then check: 242 ÷ 10 parks = 24.2 trees per park ✓

What if I set up the equation differently?

+

There are different ways to organize the algebra, but the key relationship must always be: total trees = average × total parks. As long as you maintain this balance, you'll get the right answer.

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