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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Two coworkers picked up some writing instruments at the office supply store. Abdul selected boxes of pencils and boxes of ballpoint pens, paying . Next, Ezra spent on boxes of pencils and boxes of ballpoint pens. How much does a box of each cost?A box of pencils costs _____, and a box of pens costs _____.
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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Two coworkers picked up some writing instruments at the office supply store. Abdul selected boxes of pencils and boxes of ballpoint pens, paying . Next, Ezra spent on boxes of pencils and boxes of ballpoint pens. How much does a box of each cost?A box of pencils costs _____, and a box of pens costs _____.
- Define Equations: Let's denote the cost of a box of pencils as and the cost of a box of pens as . We can write two equations based on the information given:For Abdul: For Ezra: These two equations form our system of equations.
- Multiply Equations: To solve this system using elimination, we need to eliminate one of the variables. We can do this by multiplying the equations by numbers that will make the coefficients of one of the variables the same.Let's multiply the second equation by and the first equation by , so the coefficients of will be the same.
- Perform Multiplication: Now, let's perform the multiplication:
- Eliminate Variable: Next, we subtract the second equation from the first to eliminate :This simplifies to:
- Solve for P: Now, we divide both sides by to solve for P:P = (\$)\(2\)\(\newline\)So, a box of pencils costs (\$)\(2\).
- Substitute P: With the value of P known, we can substitute it back into one of the original equations to find B. Let's use the first equation:\(\newline\)\(6P + 8B = \$28\)\(\newline\)\(6*\$2 + 8B = \$28\)\(\newline\)\(12 + 8B = \$28\)
- Solve for B: Subtract \(12\) from both sides to solve for B:\(\newline\)\(8B = (\$)28 - (\$)12\)\(\newline\)\(8B = (\$)16\)
- Solve for B: Subtract \(12\) from both sides to solve for B:\(\newline\)\(8B = (\$)28 - (\$)12\)\(\newline\)\(8B = (\$)16\)Now, we divide both sides by \(8\) to solve for B:\(\newline\)\(\frac{8B}{8} = \frac{(\$)16}{8}\)\(\newline\)\(B = (\$)2\)\(\newline\)So, a box of pens also costs \((\$)2\).
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