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Gloria can sell apples at either the town grocery store or farmer’s market. She can earn:

$6. 50 for every 20 apples she sells to the town grocery store
$8. 25 for every 24 apples she sells at the farmer’s market

Where should she sell 10 dozen apples to make the most money, and how much more will she earn there than at the other location?

User Fareeha
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1 Answer

5 votes

Answer:

Gloria should sell at the 10 dozen apples as she'd make $41.25.

This amount is $2.25 greater than the amount she'd make from selling 10 dozen apples at the town grocery store.

Explanation:

Note that a dozen is a set of 12.

Therefore, we can determine the amount of apples in 10 dozen by multiplying the amount of dozens by the total number of apples in a dozen:

10 dozen apples = dozen quantity * amount in a dozen

10 dozen apples = 10 * 12

10 dozen apples = 120

Thus, 10 dozen of apples is 120 as 10 * 12 = 120

Step 1: Determine Gloria's earnings at the grocery store from selling 10 dozen apples:

  • We can allow x to represent Gloria's earnings from 10 dozen apples (i.e. 120) at the town grocery store

We can find Gloria's earnings from selling 10 dozens at the store by creating a proportion where:

  • one ratio relates Gloria's earnings from selling 20 apples at the town grocery store,
  • and the other ratio relates Gloria's earnings from selling 10 dozen apples at the town grocery store.

$6.50 / 20 apples = $e / 120 apples

(6.50 / 20 = e / 120) * 120

(6.50 / 20) * 120 = e

$39 = e

Thus, Gloria would earn $39 from selling 10 dozen apples at the town grocery store.

Step 2: Determine Gloria's earnings at the farmer's from selling 10 dozen apples:

  • Now, we can let y to represent Gloria's earnings, but now it represents her earnings at the farmer's market.

Similar to Step 1, we can find Gloria's earnings from selling 10 dozen apples by creating a proportion where:

  • one ratio relates Gloria's earnings from selling 24 apples at the farmer's market,
  • and the other ratio relates Gloria's earnings from selling 10 dozen apples at the farmer's market.

$8.25 / 24 apples = $y / 120 apples

8.25 / 24 = y / 120) * 120

(8.25 / 24) * 120 = y

41.25 = y

Thus, Gloria would earn $41.25 from selling 10 dozen apples at the farmer's market.

Since this is the greater amount, she should sell at the farmer's market to earn more money

Step 3: Find the difference between Gloria's earnings from selling 10 dozen apples at both the town grocery store and the farmer's market:

Finding the difference of Gloria's earnings from selling 10 dozen apples at both locations will tell us how much more she'd make at the farmer's market:

Difference = 41.25 - 39

Difference = 2.25

Thus, Gloria would make $2.25 more from selling 10 dozen apples at the farmer's market instead of at the town grocery store.

User Niry
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