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

1. I can confirm that their answer is correct

2. Latifah
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)
∵ (-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)