Question 1040788: 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
Answer by ikleyn(52878)   (Show Source):
You can put this solution on YOUR website! .
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 + 2b + 3c = 12 (1)
3a + 2b + 5c = 22 (2)
2a + 4b + 4c = 18 (3)
Do this: multiply eqn. (1) by 2 and then distract it from eqn. (2) (both sides). You will get
4c - 6c = 18 - 2*12,
-2c = -6 ---> c = 3.
Now substitute c = 3 into (1) and (2) and simplify. You will get
a + 2b = 3, (4)
3a + 2b = 7. (5)
Distract (4) from eqn. (5) (both sides). You will get
2a = 7-3 = 4 ---> a = 2.
THen from 4) 2b = 3-a = 3-2 = 1 and b =  .
Answer. a = 2, b = , c = 3.
|
|
|
