Emily purchased 3 trays of strawberry plants for a total 16.47 dollars. She also purchased 10 trays of ivy plants. If the ratio of the price per tray of strawberry plants to the price per tray of ivy plants is 3 to 2, what is the total cost of all of the plants?
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To find the total cost of all the plants, we need to determine the cost of each tray of strawberry plants and each tray of ivy plants separately.
Let's start by finding the cost per tray of strawberry plants.
We are given that the ratio of the price per tray of strawberry plants to the price per tray of ivy plants is 3 to 2. Let's assume the cost per tray of strawberry plants is 3x dollars, where x is a constant.
Therefore, the cost per tray of ivy plants would be 2x dollars.
Emily purchased 3 trays of strawberry plants, so the total cost of the strawberry plants would be 3 multiplied by 3x, which is 9x dollars.
She also purchased 10 trays of ivy plants, so the total cost of the ivy plants would be 10 multiplied by 2x, which is 20x dollars.
The total cost of all the plants can be found by adding the cost of the strawberry plants and the cost of the ivy plants:
Total cost = Cost of strawberry plants + Cost of ivy plants
Total cost = 9x + 20x
Given that the total cost is $16.47, we can set up the equation:
9x + 20x = 16.47
Combining the x terms, we get:
29x = 16.47
To solve for x, we divide both sides of the equation by 29:
x = 16.47 / 29
Using a calculator, x is approximately equal to 0.5686.
Now, we can find the total cost of all the plants by substituting x back into the equation:
Total cost = 9x + 20x
Total cost = 9 * 0.5686 + 20 * 0.5686
Total cost = 5.1174 + 11.372
Total cost = 16.4894
Rounding to two decimal places, the total cost of all the plants is approximately $16.49.