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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Mrs. McKenzie is shopping for school supplies with her children. Celine selected one-inch binder and two-inch binders, which cost a total of . Rose selected one-inch binders and two-inch binder, which cost a total of . How much does each size of binder cost?A one-inch binder costs , and a two-inch binder costs .
Full solution
Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Mrs. McKenzie is shopping for school supplies with her children. Celine selected one-inch binder and two-inch binders, which cost a total of . Rose selected one-inch binders and two-inch binder, which cost a total of . How much does each size of binder cost?A one-inch binder costs , and a two-inch binder costs .
- Define variables: Define the variables for the cost of each size of binder.Let represent the cost of a one-inch binder.Let represent the cost of a two-inch binder.
- Write Celine's equation: Write the equation for Celine's selection. one-inch binder + two-inch binders =
- Write Rose's equation: Write the equation for Rose's selection. one-inch binders + two-inch binder =
- Eliminate variable : We have the system of equations:Decide which variable to eliminate.We can choose to eliminate by multiplying the first equation by .
- Multiply and rewrite system: Multiply the first equation by and rewrite the system:This gives us:
- Add equations to eliminate x: Add the two equations to eliminate x:
- Solve for y: Solve for y:Divide both sides by :
- Substitute into first equation: Substitute into the first original equation to solve for :Subtract from both sides:
- Find and : We found: (cost of a one-inch binder) (cost of a two-inch binder)Answer the question prompt with the found values.A one-inch binder costs , and a two-inch binder costs .
