Two teachers, Mr. Donahue and Mrs. Ortiz, decide to buy mechanical pencilsand rulers for their classrooms. Mrs. Ortizbuys 50 mechanical pencils and 30 rulers for $55. Mr. Donahue buys 30 of each for $45. What was the price per mechanical pencil?What was the price per ruler?a.

Price per mechanical pencil: .

Price per ruler: .

Step-by-step explanation:

Let the cost per mechanical pencil be , and let the cost per ruler be .

Set up two equations based on the amount of money that each teacher paid.

The cost of mechanical pencils ( each) and rulers ( each) would be . That should be equal to the amount of money that Mrs. Ortiz paid. In other words, .

Similarly, the cost of mechanical pencils ( each) and rulers ( each) would be . That should be equal to the amount of money that Mr. Donahue paid. In other words, .

That gives a system of two equations:

.

Subtract the second equation for the first:

.

.

In other words, the cost of one mechanical pencil would be .

Substitute back to either equation and solve for , the cost of one ruler.

.

.

.

In other words, the cost of one ruler would be .

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