Question

Billy’s restaurant ordered 200 flowers for Mother’s Day they order carnations at one dollar,roses at $2 each,and daisies at $3 each.they ordered mostly carnations,and 20 fewer roses than daisies.The total order came to $500.How many or each type of flower was ordered?

Answer 1

Let x = carnations

Let y = roses

Let z = daisies

Total flowers = 200

And we have the following equations:

`x+y+z=200`

Regarding cost:

`1x+2y+3z=500`

20 fewer roses than daisies is given by:

`y=z-20`

We have a system of 3 equations, so we proceed to solve:

Substitute y = z - 20

`\begin{gathered} x+z-20+z=200 \\ x+2\mleft(z-20\mright)+3z=500 \end{gathered}`

Simplify

`\begin{gathered} x+2z-20=200 \\ x+2z-20+20=200+20 \\ x+2z=220 \\ \text{and} \\ x+2z-40+3z=500 \\ x+5z-40=500 \\ x+5z-40+40=500+40 \\ x+5z=540 \end{gathered}`

Subtract the two equations

`\begin{gathered} x+5z=540 \\ - \\ x+2z=220 \\ -------- \\ 0+3z=320 \end{gathered}`

Solve for z

`\begin{gathered} (3z)/(3)=(320)/(3) \\ z=107 \end{gathered}`

Then substitute z in y = z - 20

`y=107-20=87`

Next, solve for x in the first equation

`\begin{gathered} x+87+107=200 \\ x+194=200 \\ x+194-194=200-194 \\ x=6 \end{gathered}`

Answer:

carnations = 6

roses = 87

daisies = 107