how to write a system of equations to describe the situation,solve using any method.

Question

Carmen is creating beaded jewerly to give to her family and friends.For her family,she assembled 1 bracelet and 2 necklaces,using total of 179 beads.For her friends,she assembled 1 bracelet and 4 necklaces,using a total of 321 beads.assuming she uses a consist number of beads for every bracelet and necklace,how many beads is she using for each?

Answer 1

Let x = the number of beads per bracelet

Let y = the number of beads per necklace

 

Using these variables, we can set up 2 equations.  The equations will represent the total number of beads.

 

x + 2y = 179   ----->  family         [1]

x + 4y = 321   ----->  friends        [2]

 

When we have more than one linear equation with more than one variable, we have a system of equations.  When solving a system of equations, we use the elimination or substitution method to reduce the number the equations and variables to work with because we can only solve one equation with one variable.

 

Note that the coefficient of x is the same for both equations.  So we can use the elimination method to get rid of x.  Subtract the second equation from the first equation.

 

-2y = -142

 

Solve for y from this equation. 

 

 

Divide both sides of the equation by -2.

 

y = 71

 

This means that Carmen uses 71 beads for every necklace.  To find the number of beads she uses for every bracelet, substitute this value of y into the first equation and solve for x.

 

x + 2(71) = 179

 

Solve for x from this equation.  This will give the number of beads she uses for every bracelet.

Answer 2

Hello JECS,

 

b = # beads in a bracelet

n = # beads in a necklace

 

From the first sentence, we have

b + 2n = 179 or

b = 179-2n

 

From the 2nd sentence

b + 4n = 321

 

So our system of equations is

b + 2n = 179

b + 4n = 321

 

Since b = 179-2n, we can use substitution and use this value of b in the 2nd equation

179-2n + 4n = 321

 

Combining terms and solving for n

2n = 142

n = 71

 

Since b = 179-2n

b = 179-2(71) = 37

 

So 71 beads were used for each necklace. 37 beads were used for each bracelet.