Hi all please help to solve this word problem. Tommy bought 3 pens and 4 magazines for $53.20. Harriet bought 5 similar pens and 3 similar magazines for $46.50. How much does 1 pen cost? Thanks

Answer 1

p = price of pens

m = price of magazines

Set equations up

Tommy (Eq. 1): 3p + 4m = 53.20

Harriet (Eq. 2): 5p + 3m = 46.50

Multiple first equation by 5 and second equation by 3. Subtract equation from equation 1.

(5)(3p + 4m = 53.20) = 15p + 20m = 266

(3)(5p + 3m = 46.50) = 15p + 9m = 139.5

Then,

(15p + 20m = 266)

- (15p + 9m = 139.5)

11m = 126.5

m = 11.5

Plug m into one of the equations to find the value of p. I'll plug it into equation 1 for this case.

3p + 4 (11.5) = 52.30

3p + 46 = 53.20

3p = 7.2

p = 2.4