Question Number 10294 by Tawakalitu ayo mi last updated on 02/Feb/17

A student needs at least three notebooks and  three pencils. Notebooks cost #60 and pencil  #36 and the student has #360 to spend. The  student decides to spend as much as possible  of his #360.  (a) How many ways can he spend his money  (b) Does any of the ways give him change ???  if so, how much ?

Answered by mrW1 last updated on 02/Feb/17

for 3 notebooks and 3 pencils:  3×60+3×36=288    money left:  360−288=72    there are 2 ways to spend this money:  way 1: to buy 2 additional pencils for 2×36=#72  way 2: to buy 1 additional notebook for #60.    way 2 gives ihm a change of #12.

Commented byTawakalitu ayo mi last updated on 02/Feb/17

wow, God bless you sir.

Answered by sandy_suhendra last updated on 02/Feb/17

let the notebooks he gets=x  and the pencils he gets=y  the linear programs are :  x≥3 , y≥3  60x+36y≤360 ⇒ 5x+3y≤30  if x=3 ⇒ 15+3y≤30                       he gets y=5 (no change)  if x=4 ⇒ 20+3y≤30                   he only gets y=3                   the change=#360−(4×#60+3×#36)=#12  if x=5 ⇒ 25+3y≤30 ⇒ y<3

Commented byTawakalitu ayo mi last updated on 02/Feb/17

wow, God bless you sir.

Answered by arge last updated on 03/Feb/17

    a=No of notebooks=3  b=No of pencils=3  x=cost of each notebooks=60  y=cost of each pencil=36  z=money of students=360    ax+by=360  3!x+3!y=360  3×2×1x+3×2×1y=360    3x+3y  3x+2y  3x+y  2x+3y  2x+2y  2x+y  x+3y  x+2y  x+y    could be 9 ways,but:    360−(2x+3y)=132, not    Rta: 8 ways

Commented byTawakalitu ayo mi last updated on 03/Feb/17

God bless you sir.