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 =.='

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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