Question

jackies broker charges her a commission of $8 per ten shares of stock she buys or sells. if jackie buys 77 shares of alesia insurance at $10.34 per share and 120 shares of ergar appliances at $8.11 per share, how much will jackie spend in commission?
a. $796.18
b. $157.60
c. $973.20
d. $1,926.98

Explanation:

Step1: Calculate total shares

First, find the total number of shares Jackie buys. For Alesia Insurance, she buys 77 shares, and for Ergar Appliances, 120 shares. So total shares = 77 + 120 = 197 shares.

Step2: Determine commission per 10 shares

The commission is $8 per 10 shares. We need to find how many groups of 10 shares are in 197, and then calculate the commission.
First, find the number of 10 - share groups: $\lceil\frac{197}{10}
ceil$ (we use ceiling function because even if there's a fraction of 10 shares, she still has to pay the commission for that partial group). $\frac{197}{10}=19.7$, so the ceiling of 19.7 is 20.

Step3: Calculate total commission

The commission per 10 - share group is $8, and there are 20 groups. So total commission = 20×8 = $160? Wait, maybe I made a mistake. Wait, let's check again. Wait, maybe the problem is that we calculate the commission for each stock purchase separately.
Wait, let's re - do:
For Alesia Insurance: 77 shares. Number of 10 - share groups: $\lceil\frac{77}{10}
ceil=\lceil7.7
ceil = 8$. Commission for Alesia: 8×8 = $64? Wait, no, the commission is $8 per ten shares. Wait, the rate is $8 for every 10 shares. So for 77 shares: 77 divided by 10 is 7.7, so we need to pay for 8 groups of 10 shares (because 7×10 = 70, and 77 - 70 = 7, so we need 8 groups to cover 77 shares). So commission for Alesia: 8×8 = $64? Wait, no, the commission per 10 shares is $8. So for 77 shares: the number of 10 - share units is 77/10 = 7.7, so we round up to 8. So commission for Alesia: 8×8=$64? Wait, no, $8 per 10 shares, so for 8 groups of 10 shares (80 shares), the commission is 8×8 = $64? But she only bought 77 shares. Wait, maybe the broker charges for the number of 10 - share increments, so even if it's less than 10, you pay for a full 10.
For Ergar Appliances: 120 shares. 120/10 = 12. So commission for Ergar: 12×8 = $96.
Then total commission: 64+96 = $160. But the options have $157.60. Wait, maybe we don't use the ceiling function, but just calculate the actual number of 10 - share groups as the number of times 10 goes into the number of shares, with a fraction. Wait, maybe the problem is that the commission is $8 per ten shares, so the rate is $0.8 per share (8/10 = 0.8). Let's try that.
For Alesia: 77 shares. Commission: 77×0.8 = $61.6
For Ergar: 120 shares. Commission: 120×0.8 = $96
Total commission: 61.6+96 = $157.6. Ah, that makes sense. Because $8 per 10 shares is equivalent to $0.8 per share. So 77×0.8 = 61.6, 120×0.8 = 96, and 61.6+96 = 157.6. Yes, that matches option b.
So let's do it this way:
Commission rate per share: $8/10 = $0.8 per share.
Total number of shares: 77 + 120 = 197 shares.
Total commission: 197×0.8 = 157.6.

Answer:

b. $157.60