Question

mia is making a necklace using two types of beads. buying 40 blue beads and 20 silver beads will cost $10. buying 20 blue beads and 60 silver beads will cost $14. how much does each type of bead cost? (x = blue, y = silver)

Explanation:

Step1: Set up system of equations

Let $x$ = cost of 1 blue bead, $y$ = cost of 1 silver bead.

$$\begin{cases} 40x + 20y = 10 \\ 20x + 40y = 14 \end{cases}$$

Step2: Simplify first equation

Divide first equation by 20:
$2x + y = 0.5$
Rearrange to isolate $y$:
$y = 0.5 - 2x$

Step3: Substitute into second equation

Substitute $y=0.5-2x$ into $20x + 40y = 14$:
$20x + 40(0.5 - 2x) = 14$
Expand and simplify:
$20x + 20 - 80x = 14$
$-60x = 14 - 20$
$-60x = -6$

Step4: Solve for x

Calculate value of $x$:
$x = \frac{-6}{-60} = 0.1$

Step5: Solve for y

Substitute $x=0.1$ into $y=0.5-2x$:
$y = 0.5 - 2(0.1) = 0.5 - 0.2 = 0.3$

Answer:

Each blue bead costs $\$0.10$, each silver bead costs $\$0.30$ (Solution $(0.1, 0.3)$)