HELP!!! i dont understand this math problem =.=?

Audree purchased two colors of wild flowers. The blue flowers cost $1 for each package and the pink flowers cost $2 for each package. How many packages of each flower did Audree buy if she paid $14 for a total of 9 packages of wildflowers











I am clueless on how to solve this!! Help me plllzzzzzzz =.=%26#039;

HELP!!! i dont understand this math problem =.=?
First set up a system of equations.


x = # of packages of blue flowers


y = # of packages of pink flowers





x + y = 9 [because there are 9 total packages]


x + 2y = 14 [total cost of all packages]





Solve for one variable and substitute.


x + y = 9


x = 9 - y





Plug into the other equation.


x + 2y = 14


(9 - y) + 2y = 14


9 + y = 14


y = 5





Now plug y into one of the original equations to find x.


x + y = 9


x + 5 = 9


x = 4





The answers are: 4 packages of blue and 5 packages of pink flowers. If you want, you can check your answers. Hope this helps!
Reply:I would try setting up a system of equations with one variable for each kind of flower.
Reply:x + 2(9--x) = 14 =%26gt; x = 4, 9--x = 9--4 = 5


4 blue and 5 pink.
Reply:b = # of blue flowers





p = # of pink flowers





total of 9 packages of wildflowers





1) b + p = 9


b = 9 - p





if she paid $14





2) 1b + 2p = 14





1(9 - p) + 2p = 14 {substitute for b from equation 1}





9 - p + 2p = 14





p = 5





Then





b = 9 - 5 = 4





Check





1(4) + 2(5) = 14


4 + 10 = 14


14 = 14
Reply:she bought 5 pink packages of flowers and 4 blue packages of flowers
Reply:[[[The person above me wrote almost the exact same thing.]]]





Say b is the number of blue flowers she bought and p is the number of pink flowers she bought.





2p + b = 14


and


p + b = 9


p = 9 - b





2(9-b) + b = 14


18-2b+b = 14


18-b = 14


b = 4


p = 9 - b = 9 - 4 = 5





She bought 4 blue and 5 pink packages.
Reply:Later on you may learn that this is involves diophantine equations (values are all integers)





Her cost was $1 x Blue + $2 x Pink = $14





You also know that Blue + Pink = 9 packages





These are simultaneous equations and may be solved by subtracting one from another. Set the equations one over the other and subtract like terms.





(B + 2P = 14)


-(B + P = 9)


= 0 + P = 5





P equals 5 (she bought 5 pinks)


Therefore she bought 9-5 = 4 blues





5 pinks at $2 = $10


4 blues at $1 = $ 4
Reply:He bought 4 packages of blue flowers and 5 packages of pink flowers.
Reply:Well there is two ways of working it out:





1) Trial and error, so if it was 1 blue flower and 1 pink flower, how much would it cost. What about 2 blue flowers and 1 pink flower? etc, until you get to $14, or pounds as we say in England! :-)





2) Use algebra! Let b=number of blue flowers and p=number of pink flowers, then youve got both these equations;


-%26gt; 1b+2p=14 (ie: blues cost $1 and pinks cost $2, total cost adds up to $14.


-%26gt; b+p=9 (ie: the amount of blues add amount of pinks is the total packages which is 9)





Then you use whatever method you are tought of solving this problem (its a simultaneous equation. Substitution?)





Answer: blues = 4, pink = 5


Check!!! -%26gt; 4x$1 + 5x$2 = 14 as well as 4+5=9!
Reply:Let x represent blue flowers


Let y represent pink flowers





1x + 2y = 14 %26lt;-- equation for price


x + y =9 %26lt;-- equation for total flowers bought.


---------------


Subtracting both equations, we get y= 5 (x cancels out)


We also know that x + y = 9 so we can solve for x knowing y


x + (5) = 9


x=4





So Audree bought 4 blue flowers and 5 pink flowers.





[Answer: Audree bought 4 blue flowers and 5 pink flowers]
Reply:OK





Two equations - two unknowns:





Let x be number of packages of blue flowers


Let y be number of packages of pink





x + y = 9 packages --- AND





$1x + $2y = $14 SO........





x +2y = 14


x+ y = 9 ; subtract the bottom from the top





y = 5





Now substitute -


x + 5 = 9


x = 4





Now check





4($1) + 5($2) = $14??


4 + 10 = 14??


14 = 14





Hope that helps.
Reply:blue flowers=b


pink flowers=p





b+2p=14


b+p=9





b=14-2p





14-2p+p=9


-p=9-14


p=5





b=14-2(5)


b=14-10


b=4



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