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Kyle is getting some flowers for Olivia, his Valentine. Being of a precise analytical mind, he plans to spend exactly \(24 on a bunch of exactly two dozen flowers. At the flower market they have lilies (\)3 each), roses (\(2 each), and daisies (\)0.50 each). Kyle knows that Olivia loves lilies; what is he to do?

Short Answer

Expert verified

Kyle would buy bouquet of $24consisting of 3lilies, 3roses and 18daisies.

Step by step solution

01

Represent the data in terms of equations.

Let 鈥榣鈥 represents the number of lilies, 鈥榬鈥 represents the number of roses and 鈥榙鈥 represents the number of daisies.

The sum of number of flowers should be equal to.24

The equations are,

l+r+d=24鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌......(1)3l+2r+0.5d=24鈥夆赌夆赌夆赌夆赌夆赌......(2)

Perform the operation on equations, 3(1)(2)

3l+3r+3d=723l+2r+0.5d=24r=482.5d鈥夆赌夆赌夆赌夆赌夆赌夆夆赌夆赌夆赌夆赌夆赌夆夆赌夆赌夆赌夆赌夆赌夆......(3)

Perform the operation on equations,2(1)(2) .

2l+2r+2d=483l+2r+0.5d=24l=24+1.5d鈥夆赌夆赌夆赌夆赌夆赌夆夆赌夆赌夆赌夆赌夆赌夆夆赌夆赌夆赌夆赌夆赌夆......(4)

02

Find the values of the variables. 

Choose the value of 鈥榙鈥 such that the values of 鈥榣鈥 and 鈥榬鈥 are positive.

Using trial and error method, the value should be, d=18

Substitute this value in the equations (3) and (4)

r=482.5(18)r=3

l=24+1.5(18)l=3

Verification:

l+r+d=243+3+18=2424=24

The number of lilies, roses and daisies are,l=3,r=3,d=18 .

Hence, Kyle would buy a bouquet of $24consisting of 3lilies, 3roses and 18daisies.

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Most popular questions from this chapter

LetS(t) be the length of the tthday of the year2013 in Mumbai (formerly known as Bombay), India (measured in hours, from sunrise to sunset). We are given the following values ofS(t) :


[tS(t)4711.5741227312]

For exampleS(47)=11.5, means that the timefrom sunrise to sunset on February16is11hours and30minutes. For locations close to the equator, the functionS(t) is well approximated by a trigonometric functionof the form

S(t)=a+bcos(2t365)+csin(2t365)

(The period is 365 days, or 1 year.) Find this approximationfor Mumbai, and graph your solution. Accordingto this model, how long is the longest day of the year inMumbai?

Find the polynomial f(t) of degree 3 such that f(1)=(1),f(2)=5,f'(1)=2,and f'(2)=9, where f'(t) is the derivative of f(t). Graph this polynomial.

Find all the vectors in R4that are perpendicular to the three vectors

[1111],[1234],[1997]

See exercise 36.

Consider a solutionx1of the linear systemAx=b. Justify the facts stated in parts (a) and (b):

a. Ifxhis a solution of the systemAx=0, thenx1+xh is a solution of the systemA=x=b.

b. Ifx2is another solution of the systemAx=b, thenx1+xhis a solution of the system Ax+0.

c. Now suppose A is a22matrix. A solution vectorx1of the systemAx+bis shown in the accompanying figure. We are told that the solutions of the systemAx=0form the line shown in the sketch. Draw the line consisting of all solutions of the systemAx=b.

If you are puzzled by the generality of this problem, think about an example first:

A=(1鈥呪赌呪赌呪赌23鈥呪赌呪赌呪赌6),b=[39]andx1=[11]

In Exercises19through 24 , find the matrix Bof the linear transformation T(x鈬赌)=Ax鈬赌 with respect to the basis I=(v1鈬赌,v2鈬赌). For practice, solve each problem in three ways: (a) Use the formula B=S-1AS , (b) use a commutative diagram (as in Examples 3 and 4), and (c) construct 鈥渃olumn by column.鈥

localid="1664194720187" A=(0110);v1鈬赌=[11];v2鈬赌=[1-1]

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