Calculating individual sales

[Simwill]

A flooring company with 4 locations sold 300,000 tiles last month. Location A sold the second most tiles. Location B accounted for 40% of total sales. Location C sold 15,000 fewer tiles than Location A. Location D sold exactly 1/5 the amount of tiles as Location C. How many tiles was sold by each location?

 

[Otis]

Hi Simwill. You've posted your question on the Arithmetic board. I'm wondering whether you're allowed to use algebra (that would be easier).

Either way, what are your thoughts so far about this exercise? Have you tried anything yet?

?

 

[Otis]

For an arithmetic approach, I would begin by working with thousands -- as if there were 300 crates containing a thousand tiles each. In other words, I would use 300 instead of 300000 (so I will multiply my results for A,B,C,D by 1000 at the end).

B is the largest number because A is second-largest and C,D are each less than A.

Calculate B: 40% of 300 is 120

300-120=180

Therefore, A,C,D must add up to 180.

Now we start making educated guesses, followed by checking.

C is smaller than A by only 15, so they are close. D is one-fifth of C, so it's much smaller than A.

Half of 180 is 90, so it would make sense to start guessing (for A) with numbers that are a bit smaller than 90 because A+C+D is 180 and A is relatively close to C.

Also, I'm assuming that C (which is A minus 15) is a multiple of 5, so I'm going to start with values for A that end in 5 or 0.

First guess: A is 80

Then C is 80-15=65 and D is 65/5=13

Now we check: 80+65+13=158

The total needs to be 180. My guess for A is too small.

Second guess: A is 90

C is 90-15=75
D is 75/5=15

90+75+15=180

The guess A=90 checks, and the answer is:

B..120,000 tiles
A.....90,000 tiles
C.....75,000 tiles
D.....15,000 tiles

 

[Otis]

An algebraic approach involves solving a system of three equations.

C = A - 15000

D = C/5

A + C + D = 180000

The substitution method yields a single equation in A:

(11/5)(A) - 18000 = 180000

Solving shows A = 90000

Back-substitution yields C=75000 and D=15000

We're told that B is (0.4)(300000)

[imath]\;[/imath]

 

[Deleted member 4993]

For an arithmetic approach, I would begin by working with thousands -- as if there were 300 crates containing a thousand tiles each. In other words, I would use 300 instead of 300000 (I will multiply my results for A,B,C,D by 1000 at the end).

B is the largest number because A is second-largest and C,D are less than A.

Calculate B: 40% of 300 is 120

300-120=180

Therefore, A,C,D must add up to 180.

Now we start making educated guesses, followed by checking.

C is smaller than A by only 15, so they are close. D is one-fifth of C, so it's much smaller than A.

Half of 180 is 90, so it would make sense to start guessing with a number that's a bit smaller than 90 (for A) because A+C+D is 180 and A is relatively close to C.

Also, I'm assuming that C (which is A minus 15) is a multiple of 5, so I'm going to start with values for A that end in 5 or 0.

First guess: A is 80

Then C is 80-15=65 and D is 65/5=13

Now we check: 80+65+13=158

The total needs to be 180. My guess for A is too small.

Second guess: A is 90

C is 90-15=75
D is 75/5=15

90+75+15=180

The guess A=90 checks, and the answer is:

B..120,000 tiles
A.....90,000 tiles
C.....75,000 tiles
D.....15,000 tiles

Why did you provide COMPLETE answer before OP shared a line of work/thought ?

 

[Otis]

Why did you provide COMPLETE answer

Hi. I'd asked the OP for their thoughts about four days ago. Less than one hour after that reply, the OP had logged in and then left without saying anything -- and they haven't been back since. I posted two methods so that the thread may serve as examples for future readers.

The unwritten rule used to be that members wait one week before posting answers, when threads appear abandoned. A while back, you had told people that the threshold is now about four days. If you've changed your mind again, that's fine, but it would be good to know. (PS: It won't bother me, if you'd like to delete my posts.)

 

[Deleted member 4993]

Hi. I'd asked the OP for their thoughts about four days ago. Less than one hour after that reply, the OP had logged in and then left without saying anything -- and they haven't been back since. I posted two methods so that the thread may serve as examples for future readers.

The unwritten rule used to be that members wait one week before posting answers, when threads appear abandoned. A while back, you had told people that the threshold is now about four days. If you've changed your mind again, that's fine, but it would be good to know. (PS: It won't bother me, if you'd like to delete my posts.)

As you know, these are just "unwritten" rules - so no harm, no foul. I just thought with 0 input from OP the "full answer" was undeserving. Locally, around my residence, I observe that the students have started to expect full answer (of course the "excuse" of Covid).