Question

cassie’s broker charges her a commission of $4.25 for every ten shares of stock bought or sold. cassie buys 92 shares of hyren airlines, 130 of giaco household goods, and 126 of iwad records. hyren airlines costs $13.70 per share, giaco household goods costs $3.28 per share, and iwad records costs $8.06 per share. to the nearest dollar, how much money did cassie spend in total?
a. $3,851
b. $2,850
c. $2,702
d. $2,551

Explanation:

Step1: Calculate cost of each stock

• Hyren Airlines: \(92 \times 13.70 = 1260.4\)
• Giaco Household Goods: \(130 \times 3.28 = 426.4\)
• Iwad Records: \(126 \times 8.06 = 1015.56\)

Step2: Calculate total stock cost

Sum the above: \(1260.4 + 426.4 + 1015.56 = 2702.36\)

Step3: Calculate total shares

Total shares: \(92 + 130 + 126 = 348\)

Step4: Calculate commission

Commission per 10 shares: \(4.25\). Number of 10 - share groups: \(\lceil\frac{348}{10}
ceil = 35\) (ceiling as partial 10 - share group still charges). Commission: \(35 \times 4.25 = 148.75\)

Step5: Calculate total cost

Total cost: \(2702.36 + 148.75 = 2851.11\approx2850\) (nearest dollar) Wait, wait, recalculate commission: Wait, \(\frac{348}{10}=34.8\), so number of commissions: 35? Wait, no, the problem says "for every ten shares bought or sold", so maybe we calculate as \(\lfloor\frac{348}{10}
floor = 34\) with a partial share? Wait, no, the broker charges for every ten shares, so if you buy 92, which is 9 ten - share groups (90 shares) and 2 extra, so 10 commissions? Wait, no, the problem says "for every ten shares", so maybe it's \(\lceil\frac{92}{10}
ceil+\lceil\frac{130}{10}
ceil+\lceil\frac{126}{10}
ceil\). Let's recalculate:

• Hyren: \(\lceil\frac{92}{10}

ceil = 10\) (since 9*10 = 90, 2 left, so 10 commissions)

• Giaco: \(\lceil\frac{130}{10}

ceil = 13\) (13*10 = 130)

• Iwad: \(\lceil\frac{126}{10}

ceil = 13\) (12*10 = 120, 6 left, so 13 commissions)

Total commissions: \(10 + 13 + 13 = 36\)? Wait, no, original total shares 348. Wait, maybe the first approach was wrong. Let's re - do:

Wait, the correct way: cost of stocks + commission.

Stock cost:

Hyren: \(92\times13.70 = 1260.4\)

Giaco: \(130\times3.28 = 426.4\)

Iwad: \(126\times8.06 = 1015.56\)

Total stock cost: \(1260.4+426.4 + 1015.56=2702.36\)

Total shares: \(92 + 130+126 = 348\)

Number of 10 - share units: \(\frac{348}{10}=34.8\), so the broker charges for 35 units (since you can't have a fraction of a commission for partial 10 - share). So commission: \(35\times4.25 = 148.75\)

Total cost: \(2702.36+148.75 = 2851.11\), which is approximately 2850 (nearest dollar). Wait, but option a is 3851, no. Wait, wait, I think I made a mistake in stock cost. Wait, Hyren Airlines: 92 shares at 13.70: 9213.70. Let's calculate 9013.70 = 1233, 213.70 = 27.4, total 1233 + 27.4 = 1260.4 (correct). Giaco: 1303.28: 1003.28 = 328, 303.28 = 98.4, total 328+98.4 = 426.4 (correct). Iwad: 1268.06: 1208.06 = 967.2, 68.06 = 48.36, total 967.2+48.36 = 1015.56 (correct). Sum: 1260.4+426.4 = 1686.8+1015.56 = 2702.36 (correct). Total shares: 92 + 130 = 222+126 = 348 (correct). Commission: 348 divided by 10 is 34.8, so we need to pay for 35 commissions (since 3410 = 340, 8 left, so 35 commissions). 35*4.25 = 148.75. Total cost: 2702.36+148.75 = 2851.11, which is approximately 2850 (nearest dollar). So the answer is b. $2,850.

Answer:

b. $2,850