how many different ways can he combine snacks to total 46 cents?

Question

it is Louis' first day at summer camp, and he is selecting snacks to bring on the hike. The camp store has a limited inventory: first aid supplies, beverages, and some snacks. The snacks are in 1-ounce cell phone packages; trail mix for 132 cents, nuts for 10 cents , dried pineapple for 8 cents, and dried apricots for 4 cents. Louis has 46 cents to spend on snacks.

Answer 1

Assumption: Louis has to spend exactly 46 cents.

1. Since he has only 46 cents to spend, he can not bring trail mix

2. 10x + 8y + 4z = 46

dividing both sides by 2

5x + 4y + 2z = 23

Since RHS is odd, and LHS should also be odd (4y+2z would always be even => 5x should be odd)

therefore x can only be odd => x:1,3

CASE 1: x=1

5*1 + 4y + 2z = 23

4y + 2z = 23-5 = 18

simplifying both sides

2y + z = 9

z can take only odd values so z: (1,3,5,7,9) => 4 possible ways

CASE 2: x=3

10*3 + 4y + 2z = 46

simplifying boh sides

2y + z = 8

y can take any value from 0 to 4 => 5 possible ways

 

Total no. of ways = 4+5 = 9