Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. Beth is creating beaded jewelry to give to her family and friends. For her family, she assembled 2 bracelets and 5 necklaces, using a total of 370 beads. For her friends, she assembled 7 bracelets and 5 necklaces, using a total of 595 beads. Assuming she uses a consistent number of beads for every bracelet and necklace, how many beads is she using for each? Beth uses _____ beads for each bracelet and _____ beads for each necklace.

Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.  Beth is creating beaded jewelry to give to her family and friends. For her family, she assembled 2 bracelets and  5 necklaces, using a total of 370 beads. For her friends, she assembled 7 bracelets and  5 necklaces, using a total of 595 beads. Assuming she uses a consistent number of beads for every bracelet and necklace, how many beads is she using for each?  Beth uses _____ beads for each bracelet and _____ beads for each necklace.

Bytelearn · Accepted Answer

Equations setup: Let's denote the number of beads used for each bracelet as b and the number of beads used for each necklace as n. For her family, Beth assembled 2 bracelets and 5 necklaces, using a total of 370 beads. This gives us the equation 2b + 5n = 370.Variable elimination: For her friends, she assembled 7 bracelets and 5 necklaces, using a total of 595 beads. This gives us the equation 7b + 5n = 595.Solving for b: We now have a system of two equations. We need to eliminate one of the variables, b or n. We choose to eliminate n because its coefficients are the same in both equations.Substitute b into first equation: To eliminate n, we subtract the first equation from the second equation. This gives us 7b + 5n - (2b + 5n) = 595 - 370. Simplifying, we get 5b = 225.Solving for n: We divide both sides of the equation by 5 to solve for b. This gives us b = 225 / 5, which simplifies to b = 45.We substitute b = 45 into the first equation and solve for n. This gives us 2(45) + 5n = 370. Simplifying, we get 90 + 5n = 370.We subtract 90 from both sides of the equation to solve for n. This gives us 5n = 370 - 90, which simplifies to 5n = 280.We divide both sides of the equation by 5 to solve for n. This gives us n = 280 / 5, which simplifies to n = 56.

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