SOLUTION: Billy Restaurant ordered 200 stalks of flowers in conjunction with Mother’s Day. They ordered carnations which cost RM1.50 per stalk, roses which cost RM5.75 per stalk and dais

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Billy Restaurant ordered 200 stalks of flowers in conjunction with Mother’s Day. They ordered carnations which cost RM1.50 per stalk, roses which cost RM5.75 per stalk and dais      Log On


   

Question 1156121: Billy Restaurant ordered 200 stalks of flowers in conjunction with Mother’s Day. They
ordered carnations which cost RM1.50 per stalk, roses which cost RM5.75 per stalk and
daisies which cost RM2.60 per stalk. Of the three types of flowers ordered, the number of
carnations was the largest. Meanwhile, the number of roses was 20 stalks less than that of
daisies. The total price of the flowers is RM589.50. How many flowers of each type were
ordered?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Price multiplied by quantity equals cost. 

FLOWER        PRICE       QUANT.     COST
 
carnations       1.5        c

roses           5.75        d-20

daisies         2.6         d

TOTALS                    200          589.5

system%28c%2B%28d-20%29%2Bd=200%2C1.5c%2B5.75%28d-20%29%2B2.6d=589.5%29

system%28c%2B2d=220%2C1.5c%2B8.35d=704.5%29

substituteforc:
1.5%28220-2d%29%2B8.35d=704.5
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Answer by ikleyn(52824) About Me  (Show Source):
You can put this solution on YOUR website!
.

            This problem can easily be solved using only one equation for one single unknown. 


Let x be the numer of daisies.

Then the number of Roses is  (x-20), 

and the number od carnations is the rest, (200-x-(x-20) = (200 - 2x + 20) = (220-2x).


The total money equation is 

    2.60*x + 5.75*(x-20) + 1.50*(220-2x) = 589.50.


Thus you have one single equation for one unknown x.

Simplify and solve it, step by step

    2.60x + 5.75x - 115 + 330 - 3x = 589.50

    5.35x + 215 = 589.50

    5.35x = 589.50 - 215 = 374.50

        x                = 374.50%2F5.35 = 70.


ANSWER.  70 daisies, 70-20 = 50 roses and the rest flowers, 200-70-50 = 80, are carnations.

Solved.

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From the first glance,  this problem is for  3  unknowns.

But,  actually,  it can be solved using only one unknown and one single equation.

There is no need to explain that obvious fact that it reduces the volume of calculations,
reduces your efforts and diminish the chances to make errors.

Therefore,  from my post learn how to do it.


You also should learn how to recognize such problems from the first glance.

At this site,  there is a  SPECIAL  LESSON  explaining and showing different similar problems solved in the same way
    - Advanced word problems to solve using a single linear equation

Remember, that your task is not to get a correct answer, only.
Your task is to make it in a right way (!)

Happy learning (!)