Math Assignment Question Precalculus

A florist is creating 10 centerpieces. Roses cost $2.50 each, lilies cost $4 each, and irises cost $2 each. A customer plans on spending $300 on 10 centerpieces with each centerpiece containing 12 flowers, with twice as many roses as the number of irises and lilies combined.

  1. a) Write a system of linear equations that represents the situation. Then write a matrix equation that corresponds to your system.
  2. b) Find the number of flowers of each type that the florist can use to create the 10 centerpieces.

Let the roses be R, Irishes be I and Lilies be L

According to the given question

R + I + L = 10 * 12 = 120

2.50 R + 2 I + 4L = 300

R = 2(I+L) which gives R -2I -2L =0

ANd the matrix equation is

b.R + I + L = 120

2.50 R + 2 I + 4L = 300

R -2I -2L =0

Equation third gives R = 2I +2 L

Substituting the value of R in the first two equations

One hundred liters of a 50% solution of a chemical mixture is obtained by mixing a 60% solution with a 20% solution. Using a system of linear equations determine how many liters of each solution are required to obtain the 50% mixture. Solve the system using matrices.

Let amount of 60% solution be x liters, therefore amount of 20% solution is y liters .

So the equations are

0.6x +0.2 y = 0.5*100

x+ y = 100

y =100 -x

Substituting the value of y in first equation

0.6 x + 0.2(100-x) = 0.5*100

At a local store, the numbers of gallons of skim milk, 2% milk, and whole milk sold over the weekend are represented by a matrix A. Skim 2% Whole Friday 40 64 52 Saturday 60 82 76 Sunday 76 96 84 The selling prices per gallon and the profits per gallon for the three types of milk are represented by B. Selling price Profit Skim $3.45 $1.20 2% $3.65 $1.30 Whole $3.85 $1.45 a) Compute AB and interpret the result. b) Find the store’s total profit from milk sales for the weekend

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