Question

a bracelet is made of 14 red beads and 19 gold beads. A necklace is made of 84 red bead and 133 gold beads. Do the two pieces of jewelry have the same ratio of red beads to gold beads?

Answer 1

No

Explanation:

Lets find out the ratios for the bracelet and the necklace. Remember that a ratio between a and b if the relation between the amounts of a respect to the amount of b and can be written as a:b or a/b.

So, the bracelet has 14 red and 19 gold, so the ratio between red and gold is 14/19. We cannot simplify this ratio as there are not common factors between 14 and 19, because 19 is a prime number.

Now lets find out the ratio for the necklace. As there are 84 red and 133 gold the ratio will be 84/133. For this ratio to be equal to 14/19 it should be that 84 is multiple of 14 and 133 multiple of 19, and both multiples must the same, this is:

84/133 = 14/19

or

84/14 = 133/19

And we know that 84/14 = 42/7 = 6

And 133/19 = 7

So, both ratios are not equal. If we verify on a calculator we have:

14/19 = 0.743

84/133 = 0.63

Thus, we can confirm they do not have the same ratio of red to gold beads.