Paloma works part-time, 4 h per day, selling fitness club memberships. She is paid $9/h, plus a $12 commission for each 1-year membership she sells

Question

Paloma notices that her sales have a pattern: for the first 12 h of the week she sells an average of two memberships per hour and for the last 12 h of the week she sells an average of three memberships per hour. Use an organized method (e.g., chart, graph, equations) to determine when Paloma will reach a special $900 earnings goal.

Answer 1

We can take the days three at a time.

First three days, the daily pattern is 4hrs of work, wages=4*9=$36, 4*2=8 memberships sold, 8*12=$96 commission. The daily total earnings=36+96=$132. Total earnings after 3 days=3*132=$396.

Last three days, the daily pattern is 4hrs of work, wages=4*9=$36, 4*3=12 memberships sold, 12*12=$144 commission. The daily total earnings=36+144=$180. Total earnings after 3 days=3*180=$540.

After 6 days' working Paloma earns 396+540=$936, exceeding the goal of $900.

After 5 days' working she would earn: 396+2*180=$756.

The graph shows accumulated earnings against day number:

It takes 6 days for Paloma to reach her goal of $900 (she actually earns $936).

Her earnings per hour in the last 3 days= 9 (wages) + 3*12 (commission)=$45.

After 5 days' work she has to make up 900-756=$144. If her minimum working time is 1 hr she would need more than 3 hours to reach her goal after 5 days' work, because 756+135=$891. This confirms that she would have to work 6 days.

Comments

sir please check this , cant i do lilke this 

 for the first 12h, she makes 12*9+12*2*12 (hour + commission)

So that's $396

For the second 12 hours, she makes 12*9+12*3*12

So $540

That makes a total of $936, which is more than $900, so she'll make it some time during the second half of the week

So, take a step back. She makes $396 in the first half, so she only needs $504 in the second part

Each hour, she makes $9 + three commissions = $9 + $36 = $45

$504/$45 = 11.2

so 23hr and 12 min  

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I have assumed she can't break her 4-hr working period. She is committed to working 4 hours a day (part-time working). Yes, I agree she APPEARS to get exactly $900 towards the end of day 5. So technically she achieves her target of $900 at an exact point in time; but in practical terms she gets $9 an hour. There is nothing to suggest she would be paid prorata for working part of an hour. $936 is 936/900=1.04 or 4% over target, but I think they want the answer in whole hours or days. I think they're looking for an answer in days. They're not looking for an exact equivalent in time. The chart shows that 6 days is the closest time. Even an hour less would fall short of the target, as I pointed out in the last paragraph. BUT...

Another point is the commission rate. It's an AVERAGE of 3 per hour. She either gets paid a commission of $12 or she doesn't. There is no fraction for the commission. It's commission or no commission. By working less than 4 hours on the last day, she may fail to get all 12 commissions. There is nothing to suggest that the commissions are earned in equal intervals of time. She may only earn $132 commission instead of $144 in the last period of working. Your calculation doesn't take this into account. This is why the chart shows points, not a continuous line.

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ok Sir thank you . I got it