Q&A | Buy N Large

Questions and Answers

QUESTION 1:

The team at buy n large are all new and consists of the following people: Sam is a salesman; he sells $1,000 worth of items every month. Daisy is a graphic designer and she can make a new poster every 2 weeks. Jake is a janitor, and Mackenzie is an inventory manager. Rachel is the receptionist and because she is so nice she gets 4 tips a day. Patrika is the personal assistant and Margerie is their manager, who as just newly joined this week. Who makes the most money in one month, two months, what about three months (each month has 4 weeks)?

ANSWER 1:

We will start by finding how much each person makes a week. Then take that value and multiply by 4. Once we do this we can simply multiply by 2 and then 3 to get how much they make in two and three months respectively. Note we can do this for everyone except Margerie (the manager) because the money she makes grows exponentially so she makes a different amount every month. So we can start by making an equation for each person. Then we will calculate how much they make. And then finally we will see who has the highest income in the first, second, and third months.

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Sam:

Let t = total money sam makes in a month

Let i = how much money’s worth of items he sells per month

Let c = the commission he makes of each item (in decimal)

Let p = his pay per hour

Let l = length of time in hours he works a day

Let d = number of days he works a week

Equation:

t= (p*l*d*4)+(i*c)

Substituting our Values:
t=(15*15*5*4)+(1000*0.40)

t=4500+400

t=4900

Sam makes $4900 in one month so in two months he makes 2*4900 and in three months he makes 3*4900.

Sam makes:

1 month: $,4,900

2 months: $9,800

3 months: 14,700

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Daisy:

Let t = total money daisy makes in a month

Let n = number of posters she makes per month

Let p = her pay per hour

Let l = length of time in hours she works a day

Let d = number of days she works a week

Equation:

t= (p*l*d*4)+50*n

Substituting our Values:
t=(30*10*5*4)+(50*1)

t=6000+50

t=6050

Daisy makes $6050 in one month so in two months she makes 2*6050 and in three months she makes 3*6050.

Daisy makes:

1 month: $6,050

2 months: $12,100

3 months: $18,150

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Jake:

Let t = total money jake makes in a month

Let p = his pay per hour

Let l = length of time in hours he works a day

Let d = number of days he works a week

Equation:

t= (p*l*d*4)

Substituting our Values:
t=(20*4*4*4)

t=1,280

Jake makes $1280 in one month so in two months he makes 2*1280 and in three months he makes 3*1280.

Jake makes:

1 month: $1,280

2 months: $2,560

3 months: $3,840

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Mackenzie:

Let t = total money Mackenzie makes in a month

Let p = her pay per hour

Let l = length of time in hours she works a day

Let d = number of days she works a week

Equation:

t= (p*l*d*4)

Substituting our Values:
t=(7*14*7*4)

t=2,744

Mackenzie makes $2744 in one month so in two months she makes 2*2744 and in three months she makes 3*2744.

Mackenzie makes:

1 month: $2,744

2 months: $5,488

3 months: $8,232

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Rachel:

Let t = total money Mackenzie makes in a month

Let p = her pay per hour

Let l = length of time in hours she works a day

Let d = number of days she works a week

Let r = number of tips she gets a day

Equation:

t= (p*l*d*4)+(2r*7*4)

Substituting our Values:
t=(14*4*7*4)+(2*4*7*4)

t=1,568+244

t=1792

Rachel makes $1792 in one month so in two months he makes 2*1792 and in three months he makes 3*1792.

Rachel makes:

1 month: $1,792

2 months: $3,584

3 months: $5,376

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Patrika:

Equation:

t= 1000

Patrika makes $1000 once and no more money after that. So $1000 is her total money paid whether that is one month or 10 years.

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Margerie:

Equation:

Let n = number of weeks

What this means:

This symbol called Sigma and it means the summation of all the numbers in a series. In our case, the series is how much she makes the first week till how much she makes the n week. And the series is an exponential one that doubles every week.

So Margerie makes:

The sum of the first month: $75

The sum of the first two months: $1,275

And the sum of the first three months: $20,475

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∴ Daisy made the most money the first and second month but Margerie made the most money the third month.

QUESTION 2:

The manager is very sick and needs to be operated on. The surgery costs $500,000. Her team wants to sponsor her surgery. They all give her half their income (including bonus, tips, decisions ect...). How many weeks will it take for them to earn enough money to fully sponsor her operation? Note: everyone gets paid at the end of the week

ANSWER 2:

We can use the numbers we generated from question 1 then we can see how many weeks it will take for them to earn $500,000. We will add all their pays together then divide it by 2 and then multiply it by x and set it equal to 500,000 and finally solve for x, thereby giving us how many months it will take for them to earn that much. The exception to this is Patrika who only gets paid once so she is separate.

x{(R+M+J+D+S)/A}+P=T

x{(1792+2744+1280+6050+4900)/2}+1,000=500,000

x{(16,766)/2}+1000=500,000

x{8383}+1000-1000=500,000-1000

8383x/8383=499000/8383

x=59.525

Since they get paid at the end of the month they will need 60 months or 5 years to earn $500,000. We can check by substituting x into our formula. I will use the shortened formula as it is equivalent to the longer version. (8383x=499000 is the same as x{(1792+2744+1280+6050+4900)/2}+1,000=500,000)

8383*60=5000000

502980=5000000

Although it is not exactly we should expect this as they do not get paid in the middle of a month but rather at its end. So they will have to work for an extra half month and by doing so will have earned a little bit more if we instead plugin (499000/8383) we will get exactly 500000.

∴ It will take 60 months for them to earn at least $500,000