SOLUTION: Sandy held garage sale during w/c she charged a dime for everything but accepted a nickel if a buyer bargained well. At the end she had sold 12 items and had a total of 95 cents. S

Algebra ->  Test -> SOLUTION: Sandy held garage sale during w/c she charged a dime for everything but accepted a nickel if a buyer bargained well. At the end she had sold 12 items and had a total of 95 cents. S      Log On


   

Question 344403: Sandy held garage sale during w/c she charged a dime for everything but accepted a nickel if a buyer bargained well. At the end she had sold 12 items and had a total of 95 cents. She only had nickels & dimes. How many of each did she have? Pls I need the equation
Found 2 solutions by josmiceli, Theo:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=number of items that she sold for a nickel
Then 12+-+x = number of items that she sold for a dime
given:
5x+%2B+10%2A%2812+-+x%29+=+95
5x+%2B+120+-+10x+=+95
-5x+=+-25
x+=+5
12+-+x+=+12+-+5
12-+5+=+7
She sold 5 items for a nickel and 7 items for a dime
check:
5x+%2B+10%2A%2812+-+x%29+=+95
5%2A5+%2B+10%2A%2812+-+5%29+=+95
25+%2B+10%2A7+=+95
25+%2B+70+=+95
95+=+95
OK

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
Total Sale was 12 items for 95 cents.
She received dimes and nickels only.
Let x = number of dimes and y = number of nickels.
Each dime was worth 10 cents.
Each Nickel was worth 5 cents.

Formula is 10*x + 5*y = 95 cents for the money.
Formula is x + y = 12 for the quantity of items sold.

You have 2 equations that need to be solved simultaneously which means that the same solution is used to solve both equations.

Solve for y in the second equation to get y = 12 - x
Substitute for y in the first equation to get 10*x + 5*(12-x) = 95
Solve for x in the first equation:
First equation is 10*x + 5*(12-x) = 95
Expand this equation to get:
10*x + 60 - 5*x = 95
Combine like terms to get:
5*x + 60 = 95
Subtract 60 from both sides of this equation to get:
5*x = 35
Divide both sides of this equation by 5 to get:
x = 7.
Use x = 7 in either equation to solve for y.
In the equation x + y = 12, substitute for x to get:
7 + y = 12
Subtract 7 from both sides of the equation to get:
y = 5
Your answer should be:
x = 7
y = 5
Substitute for x and y in both equation to see if they hold true.
x + y becomes 7 + 5 which equals 12 which is true.
10*x + 5*y becomes 10*7 + 5*5 becomes 70 + 25 which equals 95 which is also true.
The original equations hold true with the values of x = 7 and y = 5 so you have a valid solution to both equations at the same time.