Question

Teo makes a necklace of x wooden beads at .50 each and 6 glass beads at 1.25 each. The average cost of the beads in the necklace is .75. What is an equation that will model this solution?

Answer 1

For a necklace.
There are x wooden beads at $0.50 each.
There are 6 glass beads at $1.25 each

Therefore the cost of the beads in a necklace is
0.50x + 6*1.25 = 0.5x + 7.5 dollars

There are (x+6) beads. Because the average cost of the beads is $0.75, therefore
$\frac{0.5x+7.5}{x+6} =0.75 \\\\ 0.5x+7.5=0.75(x+6)$

The solution for x may be obtained as follows:
0.5x + 7.5 = 0.75x + 4.5
-0.25x = -3
x = -3/-0.25 = 12

Answer:
The equation to find x is
(0.5x + 7.5) = 0.75(x + 6)