A shopper buys 100 items for $100.00. The items include at least one................How many of each did he buy?

Question

A shopper buys 100 items for $100.00.
The items include at least one (Toilet Paper),
one (Loaf of Bread), and one (Hand Sanitizer) but no other kind.
If a Toilet Paper costs $10.00,
a Loaf of Bread costs $3.00,
and a Hand Sanitizer costs $0.50,
How many of each did he buy?

Answer 1

Toilet Paper- 5, Loaf of Bread - 1, Hand Sanitizer- 94

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Toilet Paper- p = $10
Loaf of Bread - b= $3
Hand Sanitizer- s=$0.5
p+b+s=100 --------> (1)
0.5s+3b+10p=100 --------> (2)
2*(2)-(1)=> s+6b+20p-(s+b+p)=100 => 5b+19p=100 => it has one positive integer solution: p=5, b=1 and as per (1), s=100-5-1=94
Answer:
Toilet Paper- 5*$10=$50, Loaf of Bread - 1*$3= $3, Hand Sanitizer- 94*$0.5=$47

Answer 2

$10 X 5=50
$3 X1= 3
$0.50X94=47