Kekulani purchased x cards from an artist who charges $4 per card plus $10 for personalizing the order. She is charged 7% tax on the purchase before a $5.30 shipping fee is added. Micah purchased the same number of cards from an artist who charges $4 per card plus $5 for personalizing the order. He is charged 8% tax on the purchase before an $8.60 shipping fee is added.

If each person paid the same amount, which equation could be used to determine how many cards, x, each person purchased?

Question

Kekulani purchased x cards from an artist who charges $4 per card plus $10 for personalizing the order. She is charged 7% tax on the purchase before a $5.30 shipping fee is added. Micah purchased the same number of cards from an artist who charges $4 per card plus $5 for personalizing the order. He is charged 8% tax on the purchase before an $8.60 shipping fee is added.

If each person paid the same amount, which equation could be used to determine how many cards, x, each person purchased?

anonymous · Answer

@shinalcantara

shinalcantara · Answer

Kekulani:
'x' is the number of cards
(4x + 10)(1.07) + 5.30 = amount     -----equation 1
Micah:
(4x + 5)(1.08) + 8.60 = amount    -----equation 2
since they paid the same amount then you can equate equations 1 and 2
(4x + 10)(1.07) + 5.30 = (4x + 5)(1.08) + 8.60
4x(1.07) + 10(1.07) + 5.30 = 4x(1.08) + 5(1.08) + 8.06
4.28x + 10.7 + 5.30 = 4.32x + 5.4 + 8.06
solve for x

anonymous · Answer

63.5 ?

shinalcantara · Answer

i think i got that value but lemme recheck it's impossible to have 0.5 as a number of piece of a card lol

anonymous · Answer

a. 1 + 0.07(4x + 10 + 5.30) = 1 + 0.08(4x + 5 + 8.60)
b. 1 + 0.07(4x + 10) + 5.30 = 1 + 0.08(4x + 5) + 8.60
c. 1.07(4x + 10) + 5.30 = 1.08(4x + 5) + 8.60
d. 1.07(4x + 10 + 5.30) = 1.08(4x + 5 + 8.60)

shinalcantara · Answer

c

shinalcantara · Answer

though it's kinda weird to have the number of pieces in decimal but it's how it's done so yeah it's 63.5