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, x, commax, and the number of necklaces made, yy
give coordinates
Let's assume that x represents the number of bracelets made, and y represents the number of necklaces made.
From the information given, we can create two equations:
1) The total number of bracelets and necklaces made is 14:
x + y = 14
2) The total amount of gold used is 120 grams:
4x + 20y = 120
To graphically solve this system of equations, we can plot the two equations on a graph and find their intersection point, which will give us the values of x and y.
1) For the equation x + y = 14, we can rewrite it as y = 14 - x.
We can plot this as a straight line with x as the x-axis and y as the y-axis. Choose a few values for x, and find the corresponding values for y:
(x, y)
(0, 14)
(5, 9)
(10, 4)
(14, 0)
2) For the equation 4x + 20y = 120, we can simplify it by dividing both sides by 4, giving us x + 5y = 30.
We can rewrite this equation as y = (30 - x)/5.
Again, choose a few values for x, and find the corresponding values for y:
(x, y)
(0, 6)
(5, 5)
(10, 4)
(15, 3)
Now, we can plot both lines on the same graph and find their intersection point.
The coordinates of the intersection point represent the values of x and y that satisfy both equations. In this case, the intersection point is (10, 4), which means the jeweler made 10 bracelets and 4 necklaces.