Question Eddie purchased 15 boxes of paper clips and 7 packages of index cards for a total of $55.40. Finn bought 12 boxes of paper clips and 10 packages of index cards for $61.70. Find the cost of one box of paper clips and one package of index cards

The cost of one box of paper clips is $1.85 and the cost of one package of index cards is $3.95 Step-by-step explanation: Eldora and Finn went to an office supply store together Eldora bought 15 boxes of paper clips and 7 packages of index cards for a total cost of $55.40 Finn bought 12 boxes of paper clips and 10 packages of index cards for a total cost of $61.70 We need to find the cost of one box of paper clips and the cost of one package of index cards Assume that the cost of one box of paper clips is $x and the cost of one package of index cards is $y ∵ x represents the cost of one box of paper clips ∵ y represents the cost of one package of index cards ∵ Eldora bought 15 boxes of paper clips and 7 packages of index cards for a total cost of $55.40 ∴ 15x + 7y = 55.4 ⇒ (1) ∵ Finn bought 12 boxes of paper clips and 10 packages of index cards for a total cost of $61.70 ∴ 12x + 10y = 61.7 ⇒ (2) Now we have system of equations to solve it Multiply equation (1) by -10 and equation (2) by 7 to eliminate y ∵ -10(15x) + -10(7y) = -10(55.4) ∴ -150x – 70y = -554 ⇒ (3) ∵ 7(12x) + 7(10y) = 7(61.7) ∴ 84x + 70y = 431.9 ⇒ (4) Add equations (3) and (4) ∵ (-150x + 84x) + (-70y + 70y) = (-554 + 431.9) ∴ -66x = -122.1 – Divide both sides by -66 ∴ x = 1.85 Substitute the value of x in equation (1) or (2) to find y ∵ 12(1.85) + 10y = 61.7 ∴ 22.2 + 10y = 61.7 – Subtract 22.2 from both sides ∴ 10y = 39.5 – Divide both sides by 10 ∴ y = 3.95 The cost of one box of paper clips is $1.85 and the cost of one package of index cards is $3.95 (this is an answer I got previously) Reply

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