SOLUTION: Problem: Alicia is fundraising for her soccer team by selling popcorn and cookies. She manages to sell 12 tins of popcorn and 21 tubs of cookies for a total of $320.55 on her first

Click here to see ALL problems on Linear-systems

Question 1157244: Problem: Alicia is fundraising for her soccer team by selling popcorn and cookies. She manages to sell 12 tins of popcorn and 21 tubs of cookies for a total of $320.55 on her first day of sales. The second day she ends up selling more. She sells 15 tins of popcorn and 32 tubs of cookies for a total of $447.55. What was the individual cost of each tin of popcorn and tub of cookies?
1)List the variables you will use and what they stand for. Then use those variables to create two equations which represent the problem above.
2)Solve the system of equations you created in #1 using either the elimination or substitution method. Your answers should be expressed in decimal format with correct units.
Hint: You should end up with both values of your variables.
3)Check your answers by plugging the answers for BOTH variables back into BOTH equations.

Found 2 solutions by mananth, josgarithmetic:
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
Alicia manages to sell 12 tins of popcorn and 21 tubs of cookies for a total of $320.55
Let price of individual tin of popcorn be $x number =12
and price of 21 tubs of cookies be $y. number = 21
first day of sales
Revenue = $320.55
Equation
12x+21y= 320.55------------(1)
The second day
15 tins of popcorn
and 32 tubs of cookies
total of $447.55
15x+32y=`447.55-------------(2)
Solve (1) & (2)
12.00 x + 21.00 y = 320.55

15.00 x + 32.00 y = 447.55
Eliminate y
multiply (1)by -32.00
Multiply (2) by 21.00
-384.00 x -672.00 y = -10257.60
315.00 x 672.00 y = 9398.55
Add the two equations
-69.00 x = -859.05
/ -69.00
x = 12.45
plug value of x in (1)
12.00 x + 21.00 y = 320.55
149.40 + 21.00 y = 320.55
21.00 y = 171.15
y = 8.15
Ans x = $12.45 individual tin of popcorn
y = $8.15 21 tubs of cookies
CHECK
15*12.45 +8.15*32=447.55
you check other

x

Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website!
-----------------
She manages to sell 12 tins of popcorn and 21 tubs of cookies for a total of $320.55 on her first day of sales. The second day she ends up selling more. She sells 15 tins of popcorn and 32 tubs of cookies for a total of $447.55.
-----------------

p, popcorn tins price
c, tubs of cookies price

5*E1 and 4*E2:

.
.
AND