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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Liz is creating beaded jewelry to give to her family and friends. For her family, she assembled bracelets and necklaces, using a total of beads. For her friends, she assembled bracelets and necklaces, using a total of beads. Assuming she uses a consistent number of beads for every bracelet and necklace, how many beads is she using for each?Liz uses beads for each bracelet and beads for each necklace.
Full solution
Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Liz is creating beaded jewelry to give to her family and friends. For her family, she assembled bracelets and necklaces, using a total of beads. For her friends, she assembled bracelets and necklaces, using a total of beads. Assuming she uses a consistent number of beads for every bracelet and necklace, how many beads is she using for each?Liz uses beads for each bracelet and beads for each necklace.
- Identify Equations: Identify the equations based on the given information.For the family: bracelets and necklaces use beads.For the friends: bracelets and necklaces use beads.Let represent the number of beads in a bracelet and represent the number of beads in a necklace.The equations are:
- Eliminate Variable: Decide which variable to eliminate. We can eliminate because it has the same coefficient in both equations.
- Subtract Equations: Subtract the first equation from the second to eliminate . - = - \)
- Solve for b: Solve for b.
- Substitute and Solve for : Substitute the value of back into one of the original equations to solve for . Using the first equation:
- Solve for n: Solve for n.
- Final Answer: State the final answer.Liz uses beads for each bracelet and beads for each necklace.
