Cost of two items must equal $700

Question

Karen has a set budget of $700 for flowers for the reception. Roses cost $18 per dozen and daisies cost $10 per dozen. If 50 dozen flowers are to be purchased, how many dozen of each type can be purchased to use up exactly the budgeted amount?

Answer 1

Amanda, you will find a lot of this type of word problems in your high school years and beyond.  A practical way to approach them is this:

 

Note that you have 2 categories: one is the number of items - two is the cost of the items. Set an equation for each:

 

1) The number of flowers: dozens of roses + dozens of daisies = 50 dozens; or: r + d = 50

 

2) The cost of the flowers: dozen of roses(at $18 each) + dozen of daisies(at $10 each) = $700; or: 18r+10d = 700

 

Now you have two equations.  You may easily solve them by applying any method you're familiar with:

 

1)  r + d = 50

     r = 50 - d

 

2) 18r + 10d = 700

    Substitute r with 50 - d as you found: r = 50 - d  in your previous step.

    18(50 - d) + 10d = 700

     900 - 18d + 10d = 700

     -8d = -200

     d = 25

 

d = 25 means that Karen will buy 25 dozens of daisies.  Since a total of 50 dozens are to be purchased, then Karen will buy 25 dozens of roses as well.

 

You can prove this by saying: "OK, she buys 25 dozens of roses at $18 each, that is $450; then she buys 25 dozens of daisies at $10 each, that's $250.  Yes, it is exactly $700!!

 

or:

18r + 10d = 700

18(25) + 10(25) = 700   Yes!

 

Fun. Isn't it?

    

Answer 2

Therefore 12 roses = $18 and 12 daisies = $10

 

50 dozen = 12x50= 600 flowers and they have to = $700 then

 

$18X + $10X = $700

 

$28X = $700

 

X = 25 dozen

 

to check

 

25 x $10 + 25x $18 = $250+$450 = $700

Answer 3

Let No. of a dozen Roses be R

Let No. of a dozen Daisies be D

 

Solve using simultaneous equations. 

 

First equation

 

She must spend exactly $700 dollars. Therefore: 

 

$18R + $10D = $700.00 

 

Second Equation

 

She must purchase 50 dozen flowers in any combination. 

 

R + D = 50 

 

Therefore R = 50- D

 

Substitute this into the first equation

 

$18(50-D) + $10D = $700

Expand the equation

 

$18(50-D) = 900 - 18D 

 

900- 18D + 10D = 700

900 - 700 = 18D - 10D

200 = 8D

200/8= D

25= D

 

If 25 dozen bouquets of daises must be ordered, then find how many roses must be ordered

 

Use second equation

 

R + D = 50

R + 25= 50

R - 50 - 25

R = 25