Lucy is knitting a blanket and needs to buy some more yarn. At her local craft store, 2 balls of yarn cost $7 and 8 balls of yarn cost $28. If Lucy needs 20 balls of yarn to finish... Lucy is knitting a blanket and needs to buy some more yarn. At her local craft store, 2 balls of yarn cost $7 and 8 balls of yarn cost $28. If Lucy needs 20 balls of yarn to finish the blanket, how much money will it cost?
Understand the Problem
The question describes a proportional relationship between the number of yarn balls and their cost. We need to determine the cost of 20 yarn balls based on the given information about the cost of 2 and 8 balls of yarn. We must first find the price per ball.
Answer
\$80
Answer for screen readers
$80
Steps to Solve
- Find the price per yarn ball
Since the relationship is proportional, the price per yarn ball is constant. We can determine this by finding the rate of change between the two given points: (2 balls, $8) and (8 balls, $32). We can find the price per ball (slope) $m$ using the formula:
$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
Where $x$ is the number of yarn balls, and $y$ is the cost.
$$ m = \frac{32 - 8}{8 - 2} = \frac{24}{6} = 4 $$
So, the price per yarn ball is $4.
- Calculate the cost of 20 yarn balls
Now that we know the price per ball, we can find the cost of 20 yarn balls by multiplying the number of balls by the price per ball.
$$ \text{Cost} = \text{Price per ball} \times \text{Number of balls} $$
$$ \text{Cost} = 4 \times 20 = 80 $$
Therefore, the cost of 20 yarn balls is $80.
$80
More Information
The problem demonstrates a direct proportional relationship, where the cost increases linearly with the number of yarn balls.
Tips
A common mistake is to incorrectly calculate the price per ball. For example, students may subtract the number of balls from the cost instead of dividing. Another mistake is not recognizing the proportional relationship and attempting to use more complex methods.
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