Carlotta is making blue and orange necklaces in several lengths. For each necklace, her ratio of blue beads to orange beads is 3 to 2. How many orange beads will Carlotta need for a necklace of 60 beads?

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To find the number of orange beads needed for a necklace of 60 beads, we first need to determine the ratio of blue to orange beads.

The given ratio is 3 to 2, which means for every 3 blue beads, there are 2 orange beads.

To find the number of orange beads, we need to use the ratio to set up a proportion.

Let's let x represent the number of orange beads needed for a necklace of 60 beads.

The proportion can be set up as follows:

3 blue beads / 2 orange beads = 60 blue beads / x orange beads

To solve for x, we can cross-multiply:

3 * x = 2 * 60

3x = 120

Divide both sides of the equation by 3:

x = 120 / 3

x = 40

Therefore, Carlotta will need 40 orange beads for a necklace of 60 beads.

2/5 = x/60

Cross multiply and solve for x