|
Question 89151: A university bookstore recently sold a wirebound graph-paper notebook for $2.50, and a college-ruled notebook for $2.30. At the start of spring semester, a combination of 50 of these notebooks were sold for a total of $118.60. How many of each type were sold?
A shopper buys three oranges and five lemons for $10.26, while a second shopper buys four lemons and six oranges for $11.16. What is the price of each fruit?
can i please get help with these word problems?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A university bookstore recently sold a wirebound graph-paper notebook for $2.50, and a college-ruled notebook for $2.30. At the start of spring semester, a combination of 50 of these notebooks were sold for a total of $118.60. How many of each type were sold?
:
Let x = no. of graph notebooks; Let y = no. of ruled notebooks
:
The number of items equation:
x + y = 50
or
x = (50 - y); use for substitution
:
The $$ amt equation:
2.50x + 2.30y = 118.60
:
Substitute (50-y) for x, solve for y:
2.50(50-y) + 2.30y = 118.60
:
125 - 2.5y + 2.3y = 118.60
:
-2.5y + 2.3y = 118.6 - 125
-.2y = -6.4
y = -6.4/-.2
y = 32 ruled note books
:
x = 50 - y
x = 50 -32
x = 18 graph note books
:
Check solution using $$ equation
2.5(18) + 2.3(32) = 118.6
:
:
A shopper buys three oranges and five lemons for $10.26, while a second shopper
buys four lemons and six oranges for $11.16. What is the price of each fruit?
:
Let x = price of oranges; Let y = price of lemons
:
Shopper 1 equation
3x + 5y = 10.26
:
Shopper 2 equation
6x + 4y = 11.16
:
Multiply eq1 by 2 and subtract eq2 from it:
6x + 10y = 20.52
6x + 4y = 11.16
------------------subtracting eliminates x
0x + 6y = 9.36
y = 9.36/6
y = 1.56 is the price of the lemons
:
Find x using eq1, substitute 1.56 for y:
3x + 5(1.56) = 10.26
3x + 7.80 = 10.26
3x = 10.26 - 7.80
3x = 2.46
x = 2.46/3
x = .82 is the price of oranges
:
Check solutions using eq2
6(.82) + 4(1.56) = 11.16
:
:
Did this make sense to you, any questions?
|
|
|
| |
