# a florist is making 5 identical bridesmaid bouquets for wedding. she has \$510 to spend and wants 20 flowers for each bouquet. roses cost \$4 each,tulips cost\$2 each and lilies cost \$3 each. she wants to have twice as many roses as the other 2 flowers combined in each bouquet. find total number of flowers are there

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1. For each bouquet:
Number of lilies --- x
number of tulips --- y
number of roses --- 2x + 2y , where both x and y are whole numbers

then x+y + 2x+2y = 20
3x + 3y = 20
x + y = 20/3 <----- trouble ahead: how can the sum of 2 whole numbers be a fraction?

cost per bouquet = 510/5 = 102
so 3x + 2y + 4(2x+2y) = 102
11x + 10y = 102

first one times 10
10x + 10y = 200/3
11x + 10y = 102
subtract:
x = 106/3
y = -86/3 <----- good one!

2x + 2y = -172/3

check: 3x + 3y = 3(106/3 + (-86/3) = 20
total cost: 5(3x + 2y + 4(2x+2y))
= 55x + 50y
= 55(106/3) + 50(-86/3) = 510

So my "solution" to your problem makes mathematical sense,
but not in the real world.

I could have stopped at x + y = 20/3
but I continued to show you the steps you can follow after you fix the problem.

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Reiny