Question

You have a necklace and matching bracelet with 2 types of beads. There are 30 small beads and 6 large beads on the necklace. The bracelet has 10 small beads and 4 large beads. The necklace weighs 6.6 grams and the bracelet weighs 4.2 grams. The chain has no significant weight. Find the weight of each large and small bead.

Answer 1

The weight of a small bead is 0.02 grams and the weight of a large bead is 1 gram.

Step-by-step explanation:

To find the weight of each type of bead, we need to set up a system of equations using the given information. Let's assume the weight of a small bead is x grams and the weight of a large bead is y grams.

From the information given, we can set up the following equations:

30x + 6y = 6.6 (equation 1)

10x + 4y = 4.2 (equation 2)

Now we can solve this system of equations using any method, such as substitution or elimination. Let's solve it using elimination:

Multiplying equation 1 by 2 gives us: 60x + 12y = 13.2

Multiplying equation 2 by 3 gives us: 30x + 12y = 12.6

Subtracting equation 2 from equation 1 eliminates the y terms:

60x + 12y - 30x - 12y = 13.2 - 12.6

30x = 0.6

Dividing both sides by 30 gives us: x = 0.02

Substituting the value of x back into equation 2 gives us: 10(0.02) + 4y = 4.2

0.2 + 4y = 4.2

Subtracting 0.2 from both sides gives us: 4y = 4

Dividing both sides by 4 gives us: y = 1

Therefore, the weight of a small bead is 0.02 grams and the weight of a large bead is 1 gram.