Let's carefully go through the
Grass Seed problem step by step and verify both the
table and the
solution.
---
🌿 Problem Summary:
- Kentucky Blue Grass seed costs
$5.75 per pound
- Tall Fescue seed costs
$4.50 per pound
- The nursery sells a
mixture of the two for
$5.25 per pound
- The total mixture is
5 pounds
- Let $ k $ = number of pounds of
Kentucky Blue Grass
- Then $ 5 - k $ = number of pounds of
Tall Fescue
We are to:
1. Complete the table
2. Find how many pounds of Kentucky Blue Grass ($ k $) are in the 5-pound mixture
---
✔ Part (a): Complete the Table
| | Number of Pounds | Price per Pound | Cost |
|----------------|------------------|------------------|------------------|
| Kentucky Blue Grass | $ k $ | $ 5.75 | $ 5.75k |
| Tall Fescue | $ 5 - k $ | $ 4.50 | $ 4.50(5 - k) |
| Mixture | 5 | $ 5.25 | $ 5.25 × 5 = 26.25 |
✔ So, the
cost of the mixture is:
$$
5 \times 5.25 = 26.25
$$
This matches your work — you wrote $ 5(5.25) $, which is correct.
> ⚠️ Note: You circled $ 5.25 $ in red — that’s the
price per pound, not the total cost. But the
total cost of the mixture is $ 26.25. That’s important for setting up the equation.
---
✔ Setting Up the Equation
Total cost of ingredients = Total cost of mixture
$$
\text{Cost of KBG} + \text{Cost of TF} = \text{Cost of Mixture}
$$
$$
5.75k + 4.50(5 - k) = 26.25
$$
Now solve:
$$
5.75k + 22.50 - 4.50k = 26.25
$$
$$
(5.75 - 4.50)k + 22.50 = 26.25
$$
$$
1.25k + 22.50 = 26.25
$$
Subtract 22.50 from both sides:
$$
1.25k = 3.75
$$
Divide both sides by 1.25:
$$
k = \frac{3.75}{1.25} = 3
$$
✔ So, $ k = 3 $
---
✔ Final Answer:
The nursery uses
3 pounds of Kentucky Blue Grass in the 5-pound mixture.
---
🔍 Verification:
- Kentucky Blue Grass: 3 lbs × $5.75 = $17.25
- Tall Fescue: 2 lbs × $4.50 = $9.00
- Total cost: $17.25 + $9.00 = $26.25
- Average price per pound: $26.25 ÷ 5 = $5.25 ✔️
Perfect match!
---
✔ Conclusion:
Your
work is correct!
- The table is filled correctly.
- Your equation setup and solution are accurate.
- $ k = 3 $ is the right answer.
Just make sure the
"Cost" row for the mixture shows
$26.25, not just $5.25.
---
✔ Final Answer:
$$
\boxed{3} \text{ pounds of Kentucky Blue Grass}
$$
Parent Tip: Review the logic above to help your child master the concept of weighted averages worksheet with answers.
