|
Question 1201814: A florist spent $1558 purchasing 64 bundles of flowers to make spring bouquets. The order consisted of tulips, daisies, and peonies. The peonies cost $95 a bundle, the tulips were $23 a bundle adn the daisies were $12 a bundle. The florist purchased the fewest bundles of peonies, and twice as many daisies as tulips.
a. Write a system of equations to represent the information, solve the system using elimination or substitution, and then determine the number of bundles of each flower.
Found 2 solutions by ikleyn, mananth:
Answer by ikleyn(52799)   (Show Source):
You can put this solution on YOUR website! .
A florist spent $1558 purchasing 64 bundles of flowers to make spring bouquets.
The order consisted of tulips, daisies, and peonies.
The peonies cost $95 a bundle, the tulips were $23 a bundle and the daisies were $12 a bundle.
The florist purchased the fewest bundles of peonies, and twice as many daisies as tulips.
a. Write a system of equations to represent the information,
solve the system using elimination or substitution, and then determine
the number of bundles of each flower.
~~~~~~~~~~~~~~~~~~~
Problems like this one, admit reduction to one equation in one unknown,
as I show you below. It is commonly accepted, educative and elegant method of solution.
The method using three equations and three unknowns is non-educative and most stupide.
Let x be the number of bundles of tulips.
Then the number of bundles of daisies is 2x, according to the problem,
and the number of bundles of peonies is the rest (64-x-2x) = (64-3x).
Write the total money equation
23x + 12*(2x) + 95*(64-3x) = 1558 dollars.
Simplify and find x
23x + 24x + 6080 - 195x = 1558
23x + 24x - 285x = 1558 - 6080
-238x = -4522
x =  = 19.
ANSWER. 19 bundles of tulips; 2*19 = 38 bundles of daises and 64-3*19 = 64-57 = 7 bundles of peonies.
Solved.
---------------
The part of the condition "the fewest bundles of peonies" is irrelevant to the problem - we do not use it in the solution.
My advice to the composer of this problem is to remove these words from the problem.
Also, another advise is to remove the words related to system of equations.
Then the problem will look perfectly; otherwise, it looks like a lame horse.
Answer by mananth(16946)  (Show Source):
You can put this solution on YOUR website!
A florist spent $1558 purchasing 64 bundles of flowers to make spring bouquets. The order consisted of tulips, daisies, and peonies. The peonies cost $95 a bundle, the tulips were $23 a bundle adn the daisies were $12 a bundle. The florist purchased the fewest bundles of peonies, and twice as many daisies as tulips.
a. Write a system of equations to represent the information, solve the system using elimination or substitution, and then determine the number of bundles of each flower.
A florist spent $1558, 64 bundles of flowers
tulips, daisies, and peonies.
The peonies cost $95 a bundle numbers be x
the tulips were $23 a bundle numbers be y
the daisies were $12 a bundle numbers 2y
Bundles Count equation
x+3y=64......................(1)
Cost equation
95x +23y+12*2y =1558
95x +47y =1558.................(2)
multiply equation (1) by -95 and add to equation 2
-95x-285y=-6080
ADD
-238y = -4522
y= 19 number of tulips
19*2 =38 number of daisies
(64-57) =7 peonies
7*95+38*12+19*23=1558
|
|
|
| |
