SOLUTION: I cannot figrue out this word problem help please!! Mr. Adams buys a bag or apples and a bag of pears for a total of $14. There are eight pounds of fruit in all. The apples cost

Question 59811This question is from textbook Alegbra Concepts and Applications
: I cannot figrue out this word problem help please!!
Mr. Adams buys a bag or apples and a bag of pears for a total of $14. There are eight pounds of fruit in all. The apples cost $1.50 per pound, and the pears cost $2.30 per pound. How many pounds of pears did he buy?? This question is from textbook Alegbra Concepts and Applications

Found 2 solutions by uma, joyofmath:
Answer by uma(370) (Show Source): You can put this solution on YOUR website!
Let Mr Adams buy x pounds of pears.
Total quantity bought = 8 pounds.
So quantity of apples bought = (8 - x) pounds.
Cost of 1 pound of apples= $ 1.50
So cost of (8 - x) pounds of apples = $(8-x)(1.50)
Cost of 1 pound of pears = $ 2.30
So cost of x pounds of pears = $x(2.30)
Total cost of fruits = $14
The equation becomes..
(8-x)(1.50) + x(2.30) = 14
==> 12 - 1.50x + 2.30x = 14 [Removing the4 parenthesis by multiplying term by term]
==> 12 + 0.80x = 14
==> 0.80x = 14 - 12 [subtracting 12 from both the sides]
==> 0.80x = 2
==> 0.80x/0.80 = 2/0.80
==> x = 2.5
Mrs Adams bought 2.5 pounds of pears
Good Luck!!!

Answer by joyofmath(189) (Show Source): You can put this solution on YOUR website!
Let = weight of apples.
Let = weight of pears.
Let = cost per pound of apples.
Let = cost per pount of pears.
(1) Then because Mr. Adams bought 8 pounds of fruit.
(2) Also because the fruit cost $14.
(3) because apples cost $1.50 per pound.
(4) because pears cost $2.30 per pound.
In (1) we substract from both sides of the equation and get
In (2) we replace and with 1.5 and 2.3 respectively. We then get:

But, we know that so we know that
which expands to
which is equivalent to
which is equivalent to
which is equivalent to
Divide both sides by and we get
So, Mr. Adams bought 5.5 bags of apples.
He bought 8 pounds of fruit in total so he bought 2.5 pounds of pears, which is the answer to the question.
To verify the answer:
If and
Then, from (2) above
Or, should equal 14
and
and, indeed, 8.25+5.75=14
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