Whats the answer???????????????

Question

A salesperson bought a case of pens. On monday he sold half of the pens. on tuesday he sold 30 more pens. on wednesday he sold one third of the pens that were left. on thurstday he sold the remaining 40 pens. how many pens were originally in the case?

Answer 1

Start with x pens:

Monday he sold x/2 pens

Tuesday he sold 30 pens

Wednesday is trickier, but think in terms of x

He had x/2 pens left on monday then sold 30 more on tuesday

so to express the amount of pens remaining you could write (x/2 - 30) and so he sold 1/3 of these on wednesday which is

(x/2 - 30)/3

Thursday he sold 40

Since it said he sold all of his pens we can make an equation which has the total pens he began with (x) equal to the sum of the pens he sold each day

x = (x/2) + 30 + (x/2 - 30)/3 + 40

x = (x/2) + 70 + (x/6) - 10

x = (2x/3) + 60

x = 180 pens originally in case

Answer 2

180

Answer 3

Let X be the number of pens at the beginning.

On Monday he sold 1/2 of the pens, so he has 1/2 left.

Remaining = (1/2)X

On Tuesday he sold 30 more pens:

Remaining = (1/2)X - 30

On Wednesday he sold 1/3 of the pens that were left (leaving 2/3):

Remaining = (2/3)[(1/2)X - 30]

On Thursday he sold the remaining 40 pens (leaving none)

(2/3)[(1/2)X - 30] - 40 = 0

Now just solve going backwards:

Step 1:  Add 40 to both sides:

(2/3)[(1/2)X - 30] = 40

Multiply both sides by the reciprocal of 2/3 --> 3/2:

(1/2)X - 30 = (3/2)40

(1/2)X - 30 = 60

Add 30 to both sides:

(1/2)X = 90

Multiply both sides by 2:

X = 180

Double-check:

Monday:  Sold half --> 90 pens

Tuesday:  Sold 30 more --> 60 pens

Wednesday:  Sold 1/3 --> 40 pens

Thursday:  Sold all 40 of the rest --> 0 pens

Answer:

180 pencils at the beginning

Answer 4

40=2/3 of whats left of half minus 30, so

60 = whats left of half minus 30, so

90 = half, so

180 = box o pens.

180