At the school bookstore and two binders and three pens cost $12.50. Three binders and five pens cost $19.50. What is the approximate cost of 1 binder and 1 pen?
Let x = the cost of one binder and let y = the cost of one pen. The ?rst statement, "two binders and three pens cost $12.50," translates to the equation 2x + 3y = 12.50. The second statement, "three binders and ?ve pens cost $19.50," translates to the equation: 3x + 5y = 19.50
Multiply the ?rst equation by 3: 6x + 9y = 37.50
Multiply the second equation by -2: -6x + -10y = -39.00
Combine the two equations to eliminate x: -1y = -1.50
Divide by 1: y = 1.50
Thus, the cost of one pen is $1.50. Since the cost of 2 binders and 3 pens is 12.50, substitute y 1.50 within the ?rst equation: 3 × $1.50 = $4.50; $12.50 - 4.50 = $8.00; $8.00 ÷ 2= $4.00, so every binder is $4.00. The total cost of 1 binder and 1 pen is $4.00 + $1.50 = $5.50.