You buy ballpoint pens for $4.31 per box, felt pins for $3.41 and the total is $65.36. How many boxes of each type of pens did you buy?

Question

You buy ballpoint pens for $4.31 per box, felt pins for $3.41 and the total is $65.36. How many boxes of each type of pens did you buy?

Answer 1

The single equation is:

   $4.31x + $3.41y = $65.36

     where x=number of boxes of ballpoint pen

                y = number of boxes of felt tip pens

 

The only integers that fit the values of x and y so that the price is exact are:

     x = 12

     y = 4

 

(I used a computer to try all possibilities).

 

You could find the LCM (least common multiple) by finding a value that is the same in each column (the n value gives an x and a y value):

 

             4.31n   =  $65.36-$3.41n

n:                            

1           4.31           61.95

2           8.62           58.54

3           12.93         55.13

4           17.24         51.72

5           21.55         48.31

6           25.86         44.90

7           30.17         41.49

8           34.48         38.08

9           38.79         34.67

10        43.10         31.26

11        47.41         27.85

12        51.72         24.44

13        56.03         21.03

14        60.34         17.62

15        64.65         14.21

16        68.96         10.80

17                           7.39

18                           3.98

19                           0.57

20                           -2.84