Question

Sara is selling rings and bracelets online.
Today she made 5 rings and 3 braclets, using a total of 340 centimeters of copper wire.
Each bracelet needs 4 times more wire than each ring.
How much wire is needed for each piece of jewelry?
Write and solve a system of equations.

Answer 1

Answer:

20 cm of wire is needed for rings

80 cm of wire is needed for bracelets

Step-by-step explanation:

We can set up the following system of equations:

$\left\{{{5r+3b=340}\atop{b=4r}}$

Substituting b with 4r in the first equation:

$5r+3b=340$

$5r+3(4r)=340$

$5r+12r=340$

$17r=340$

$r=20$

Thus, 20 cm of copper wire is needed for each ring, and:

$b=4r$

$b=4(20)$

$b=80$

Therefore, 80 cm of copper wire is needed for each bracelet.

To verify our numbers, if Sara made 5 rings and 3 bracelets, she would need (20 cm × 5) + (80 cm × 3) = 100 cm + 240 cm = 340 cm of copper wire. This is correct.