The Greek Marketplace

Algebra Level pending

One day, a Greek entered a marketplace. He saw three apples, two oranges, and four bananas. Each apple costed one more than the difference of the $3$ bananas and $2$ oranges. ( $3$ bananas cost more than $2$ oranges). The Greek bought $1$ apple, $2$ oranges and $4$ bananas. He paid $22$ dollars. Each orange costed $\$2.75$ . What was the price of the apple?

$4.50 $4.00 $5.75 $2.75 $3.50

2 solutions

A Former Brilliant Member
Jul 17, 2017

Let $a$ be the cost of the one apple, $b$ be the cost of one banana and $c$ be the cost of one orange.

From the second sentence in the problem, the equation is

$a=3b-2c+1$ , however, $c=2.75$ , therefore $a=3b-2(2.75)+1=3b-4.5$ $\color{#D61F06}(1)$

From the third and fourth sentences in the problem, the equation is

$a+2c+4b=22$ , however, $c=2.75$ , therefore $a+2(2.75)+4b=22$ $\color{#3D99F6}\large \implies$ $a+4b=16.5$ $\color{#D61F06}(2)$

Substitute $\color{#D61F06}(1)$ in $\color{#D61F06}(2)$ . we have

$3b-4.5+4b=16.5$ $\color{#3D99F6}\large \implies$ $7b=21$ $\implies$ $b=3$

It follows that,

$a=3(3)-4.5=$ $\color{#D61F06}\large \boxed{4.5}$

Micah Gadbois
Jul 17, 2017

We assign variables. "A" stands for apple, "C" stands for orange, and "B" stands for banana.
The first requirement: A = 1+3B-2C
Thus, 1+3B-2C+2C+4B = 22
7B = 21
B = 3
Since we know C = 2.75, 2C = 5.5
4B+2C = 12 + 5.5 = 17.5
22 - 17.5 = 4.5
A = 4.5

Assigning "O" for orange is not a good idea, since "O" looks like "0" (zero). For example in the second line of your solution, "2O" means two oranges, but it looks like "20" (twenty). That's why I used the variable $c$ to represent orange in my solution for clarity.

A Former Brilliant Member - 3 years, 10 months ago

The Greek Marketplace

2 solutions

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