Some friends are planning to make a neighborhood garden. The total area available for the garden is 210 square meters, and they want this to be 1 1/3 times the area of the plant beds in the garden. What should the area of the plant beds be?

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Understand Relationship: Understand the relationship between the total area and the area of the plant beds. The total area of the garden is 1 1/3 times the area of the plant beds. This means that if we let the area of the plant beds be x square meters, then the total area is (4/3)x square meters.Set Up Equation: Set up the equation to find the area of the plant beds. We know that the total area is 210 square meters, so we can set up the equation (4/3)x = 210.Solve for x: Solve for x by multiplying both sides of the equation by the reciprocal of 4/3. To isolate x, we multiply both sides by 3/4, which is the reciprocal of 4/3. (3/4) * (4/3)x = (3/4) * 210Perform Multiplication: Perform the multiplication to solve for x. (3/4) * (4/3)x = x (3/4) * 210 = 157.5 So, x = 157.5 square meters.Check Result: Check the result. To check, we can multiply the area of the plant beds by 1 1/3 to see if we get the total area of the garden. 1 1/3 * 157.5 = (4/3) * 157.5 = 210 This confirms that our solution is correct.

Some friends are planning to make a neighborhood garden. The total area available for the garden is $210 \, \text{square meters}$ , and they want this to be $1 \frac{1}{3}$ times the area of the plant beds in the garden. What should the area of the plant beds be?

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