## Puzzle | 4 items in a store; a*b*c*d = a+b+c+d

PART 1

The price tags on three items in a store are :

$Amount=\char36 0.75$
$Amount=\char36 2.20$
$Amount=\char36 5.50$

We note that

$0.75 \; \times \: 2.00 \; \times \: 5.50 \; = \; 0.75 \; + \; 2.00 \; + \; 5.50 \; = \; 8.25$

Find four prices,   a,   b,   c,   and   d   such that

$a \; \times \: b \; \times \: c \; \times \: d \; = \; a \; + \; b \; + \; c \; + \; d \; = \; 8.25$

$Amount=\char36 0.50$
$Amount=\char36 2.00$
$Amount=\char36 2.75$
$Amount=\char36 3.00$

$0.5 \; \times \: 2 \; \times \: 2.75 \; \times \: 3 \; = \; 0.5 \; + \; 2 \; + \; 2.75 \; + \; 3 \; = \; 8.25$

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PART 2

Find four prices,   A,   B,   C,   and   D   such that

$A \; \times \: B \; \times \: C \; \times \: D \; =\; A \: + \: B \: + \: C \: + \: D \; =\; 6.75$

N.B.   there are two solutions.

math grad - Interest: Number theory
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### 1 Response to Puzzle | 4 items in a store; a*b*c*d = a+b+c+d

1. Paul says:

The two solutions are:-

1, 1.5, 2, 2.25
1.2, 1.25, 1.8, 2.5

Paul.