The table shows the number of beads used to make a necklace. Ginger wants to make a smaller necklace using the same ratio of pink to white beads. How many different necklaces could Ginger make? How do you know?
Colour Number
Pink 30
White 35
i need the answer
To determine how many different necklaces Ginger could make using the same ratio of pink to white beads, we need to find the common ratio between the number of pink and white beads in the given necklace.
In this case, the ratio of pink to white beads can be calculated as:
Ratio = Number of Pink Beads / Number of White Beads
Ratio = 30 / 35
Simplifying the ratio further, we have:
Ratio = 6/7
Now, to find the number of necklaces Ginger could make, we need to consider how many different pairs of numbers exist where the ratio of those numbers equals 6/7.
Given that Ginger wants to make a smaller necklace, where the ratio remains the same, the number of pink and white beads will have to be smaller than the original necklace.
We can use trial and error to find all the possible pairs of numbers that give us a ratio of 6/7. Let's start by finding pairs with smaller numbers:
Possible pairs:
- 6 pink beads and 7 white beads (6/7 ratio)
- 12 pink beads and 14 white beads (6/7 ratio)
- 18 pink beads and 21 white beads (6/7 ratio)
- ...
The pattern we observe is that for every pair (6x, 7x), where x is a positive integer, the ratio will always be 6/7. Since there is an infinite number of positive integers, Ginger can make an infinite number of smaller necklaces using the same ratio of pink to white beads.
Therefore, Ginger can make an unlimited number of different necklaces with the given ratio of pink to white beads.
Dua use 32 bead to make a necklace. three-fourth of the beads are purple . how many beads are purple.
GCD(30,35) = 5
(30,35) = 5*(6,7)
so any multiple of (6,7) will work, as long as it's at most (30,35)