Question

A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of

gold in each bracelet is 4 grams and the amount of gold in each necklace is 20 grams.
The jeweler made a total of 14 bracelets and necklaces using 120 grams of gold.
Graphically solve a system of equations in order to determine the number of bracelets
made, «, and the number of necklaces made, y. I need the graph

Answer 1

• 10 bracelets
• 4 necklaces

Explanation:

You want the number of bracelets (x) and the number of necklaces (y) made from 120 grams of gold when a total of 14 were made with 4 grams in each bracelet and 20 grams in each necklace.

Equations

The equations describing the numbers can be written as ...

4x +20y = 120 . . . . . . amount of gold used

x + y = 14 . . . . . . . . . number of items made

Graph

The first equation can be graphed by plotting its x-intercept at (30, 0) and its y-intercept at (0, 6). The line between these points is the graph.

The graph of the second equation is the line between the two intercepts at 14: (14, 0) for the x-intercept, and (0, 14) for the y-intercept.

The lines cross at (x, y) = (10, 4).

The number of bracelets made was 10; the number of necklaces, 4.