How many 3 sweet of pack are there?

Question

A shop seller sells 3,4and 5 pack of sweet.he have 136 pack of sweet or 516 sweet in total. Given that 3 sweet of pack and 4 sweet of pack are 3 times the 5 sweet of pack.

Answer 1

A shop seller sells 3,4and 5 pack of sweet.he have 136 pack of sweet or 516 sweet in total. Given that 3 sweet of pack and 4 sweet of pack are 3 times the 5 sweet of pack.

Let n3 be the number of 3 sweet packs.

Let n4 be the number of 4 sweet packs.

Let n5 be the number of 5 sweet packs.

 

Then n3 + n4 + n5 = 136             (he have 136 pack of sweet)

n3*3 + n4*4 + n5*5 = 516            (or 516 sweet in total)

n3 + n4 = n5*3                              (3 sweet of pack and 4 sweet of pack are 3 times the 5 sweet of pack.)

 

Substituting for n3 = n5*3 – n4 into the 1st two equations,

 

(n5*3 – n4) + n4 + n5 = 136

(n5*3 – n4)*3 + n4*4 + n5*5 = 516

 

Evaluating the above two eqns,

 

n5*4 = 136

n4 + n5*14 = 516

 

Substituting for n5 = 34 into the 2nd eqn above,

 

n4 + 34*14 = 516

n4 = 516 – 476

n4 = 40

 

Using n3 + n4 + n5 = 136

n3 + 40 + 34 = 136

n3 = 62

 

Number of 3-sweet bags = 62, Number of 4-sweet bags = 40, Number of 5-sweet bags = 34

 

Answer 2

A=3-pack, B=4-pack, C=5-pack; A+B+C=136-total packs.

3A+4B+5C=516 sweets in all.

A+B=3C so 3C+C=136, 4C=136, C=34, and A+B=136-34=102, so B=102-A.

Substitute for B and C: 3A+4(102-A)+170=516; 3A+408-4A=346; 62=A (B=102-62=40) so there are 62 3-packs of sweets.