Ratio Problem: Calculate Flowers Needed for 1:4 Proportion in 380 Pots

Q: Why doesn't the total number of pots change when we add flowers?

Great question! We're converting empty pots into flower pots, not adding brand new pots. The nursery still has exactly 380 total pots - we're just changing what's in some of them!

Q: How do I know which number goes on top and bottom of the fraction?

The ratio 1:4 means 1 flower pot for every 4 total pots. So flowers go on top (numerator) and total pots go on bottom (denominator): $ \frac{\text{flowers}}{\text{total}} = \frac{1}{4} $

Q: What if I set up the equation backwards?

If you write $ \frac{380}{40+x} = \frac{4}{1} $, that's okay! Just make sure both sides represent the same relationship. Cross multiply and you'll still get the right answer.

Ratio Equations with Cross Multiplication

In a nursery there are 380 pots, of which 40 are flowers.
How many flowers need to be added so that the ratio between flowers and all pots will be 1:4?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

In a nursery there are 380 pots, of which 40 are flowers.
How many flowers need to be added so that the ratio between flowers and all pots will be 1:4?

Step-by-step solution

The problem requires us to find out how many flowers need to be added to meet a specific ratio of flower pots to total pots.

Let's denote the additional number of flowers needed as $x$ . The current number of flower pots is 40, and we need to make the ratio of flower pots to total pots $1:4$ .

We can establish the equation based on the desired ratio:

$\frac{40 + x}{380} = \frac{1}{4}$

To solve for $x$ , cross-multiply the terms:

$4(40 + x) = 380$

Simplify and calculate:

$160 + 4x = 380$

Subtract 160 from both sides:

$4x = 220$

Now divide both sides by 4:

$x = 55$

Therefore, 55 additional flowers need to be added to achieve the desired ratio.

Comparing this result with the given answer choices, we find that the correct answer is choice 4: $55$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Set up: Write new ratio as equation: (40+x)/380 = 1/4
Cross multiply: 4(40+x) = 380 gives 160+4x = 380
Verify: Check final ratio: 95/380 = 1/4 ✓

Common Mistakes

Avoid these frequent errors

Using original total pots instead of keeping 380
Don't change the total to 380+x! The problem states we add flowers to existing pots, so total stays 380. This gives wrong equation (40+x)/(380+x) = 1/4. Always keep the original total when adding items of one type only.

Practice Quiz

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What is the ratio between the orange and gray parts in the drawing?

FAQ

Everything you need to know about this question

Why doesn't the total number of pots change when we add flowers?

Great question! We're converting empty pots into flower pots, not adding brand new pots. The nursery still has exactly 380 total pots - we're just changing what's in some of them!

How do I know which number goes on top and bottom of the fraction?

The ratio 1:4 means 1 flower pot for every 4 total pots. So flowers go on top (numerator) and total pots go on bottom (denominator): $\frac{\text{flowers}}{\text{total}} = \frac{1}{4}$

What if I set up the equation backwards?

If you write $\frac{380}{40+x} = \frac{4}{1}$ , that's okay! Just make sure both sides represent the same relationship. Cross multiply and you'll still get the right answer.

Can I solve this without using x?

You could work backwards: if flowers are 1/4 of total, then 380 ÷ 4 = 95 flowers needed. Since we have 40, we need 95 - 40 = 55 more. But using x helps organize your thinking!

How do I check if 55 is really correct?

Add the flowers: 40 + 55 = 95 flower pots. Check the ratio: $\frac{95}{380} = \frac{1}{4}$ ✓ Perfect! The ratio matches exactly what the problem asked for.

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