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

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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?

posted Apr 22

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

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
Toilet Paper- 5*\$10=\$50, Loaf of Bread - 1*\$3= \$3, Hand Sanitizer- 94*\$0.5=\$47

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

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