Juan is buying flowers for his mother. He has $18 to spend and sees that roses are $3 each and camations are $1.50 each. He wants to buy 3 times as many camations as roses and spend all of his money on Towers. Write a Ssystem of equations that models this situation. Is there a viable solution that meets Juan's conditions? Explain. 14 points)

 System of equations to model the situation is there a viable solution that means Joannes condition explain

System of Equations

3x + 1.5y = 18 Equation 1

x = 3y ... Equation 2

This is not viable

Step-by-step explanation:

Let us represent

Number of roses = x

Number of camations = y

Juan is buying flowers for his mother. He has $18 to spend and sees that roses are $3 each and camations are $1.50 each.

$3 × x + $1.50 × y = $18

3x + 1.5y = 18 Equation 1

He wants to buy 3 times as many camations as roses

y = 3x Equation 2

Therefore:

System of Equations

3x + 1.5y = 18 Equation 1

x = 3y ... Equation 2

This is not viable

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.