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

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> 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      Log On


   

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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
Let w%5Ba%5D = weight of apples.
Let w%5Bp%5D = weight of pears.
Let c%5Ba%5D = cost per pound of apples.
Let c%5Bp%5D = cost per pount of pears.
(1) Then w%5Ba%5D%2Bw%5Bp%5D=8 because Mr. Adams bought 8 pounds of fruit.
(2) Also c%5Ba%5D%2Aw%5Ba%5D%2Bc%5Bp%5D%2Aw%5Bp%5D=14 because the fruit cost $14.
(3) c%5Ba%5D=1.5 because apples cost $1.50 per pound.
(4) c%5Bp%5D=2.3 because pears cost $2.30 per pound.
In (1) we substract w%5Ba%5D from both sides of the equation and get w%5Bp%5D=8-w%5Ba%5D
In (2) we replace c%5Ba%5D and c%5Bp%5D with 1.5 and 2.3 respectively. We then get:
1.5%2Aw%5Ba%5D%2B2.3%2Aw%5Bp%5D=14
But, we know that w%5Bp%5D=8-w%5Ba%5D so we know that 1.5%2Aw%5Ba%5D%2B2.3%2A%288-w%5Ba%5D%29=14
which expands to 1.5%2Aw%5Ba%5D%2B2.3%2A8-2.3%2Aw%5Ba%5D=14
which is equivalent to 1.5%2Aw%5Ba%5D%2B18.4-2.3%2Aw%5Ba%5D=14
which is equivalent to -.8%2Aw%5Ba%5D%2B18.4=14
which is equivalent to -.8%2Aw%5Ba%5D=-4.4
Divide both sides by -.8 and we get w%5Ba%5D=5.5
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 w%5Ba%5D=5.5 and w%5Bp%5D=2.5
Then, from (2) above c%5Ba%5D%2Aw%5Ba%5D%2Bc%5Bp%5D%2Aw%5Bp%5D=14
Or, 1.5%2A5.5%2B2.3%2A2.5 should equal 14
1.5%2A5.5=8.25 and 2.3%2A2.5=5.75
and, indeed, 8.25+5.75=14