Question

Several customers order small fruit baskets made of apples, bananas, and oranges. Let a represent the price per pound of apples, b represent the price per pound of bananas, and c represent the price per pound of oranges. The system represents the number of pounds of each type of fruit and the total price of each fruit basket. How much per pound does each type of fruit cost?
a+2b+3c=12
3a+2b+5c=22
2a+4b+4c=18

a. a=2 , b=0.5 , c=3
b. a=2 , b=1.5 , c=3
c. a=2.5, b=0.25, c=3
d. a=2.5 , b=0.75,c=3

Answer 1

Answer: Option 'a' is correct.

Step-by-step explanation:

Let the price per pound of apples be 'a'

Let the price per pound of bananas be 'b'

Let the price per pound of oranges be 'c'.

According to question,

$a+2b+3c=12------------(1)\\\\3a+2b+5c=22--------------(2)\\\\2a+4b+4c=18-----------------(3)$

From eq (3), we can take common 2:

$2(a+2b+2c)=18\\\\a+2b+2c=\frac{18}{2}=9$

So, we can write it as :

$a+2b=9-2c$

Put it in Eq (1),

$a+2b+3c=12\\\\9-2c+3c=12\\\\9+c=12\\\\c=12-9\\\\c=3$

Put the value of c in eq(2) and (3),

$a+2b=9-2(3)\\\\a+2b=9-6\\\\a+2b=3-------------(4)\\\\and\\\\3a+2b+5c=22\\\\3a+2b+5(3)=22\\\\3a+2b=22-15\\\\3a+2b=7-------------------(5)$

So, we can write it as :

$a+2b=3\\\\2b=3-a$

Put it in equation (5), we get

$3a+2b=7\\\\3a+3-a=7\\\\2a+3=7\\\\2a=7-3\\\\2a=4\\\\a=\frac{4}{2}\\\\a=2$

Substitute the value of a to get the value of b:

$2b=3-a\\\\2b=3-2\\\\2b=1\\\\b=\frac{1}{2}=0.5$

Hence, the value of a= 2, b = 0.5, c = 3.

Therefore, Option 'a' is correct.