Question

Systeinis Applicaitons.por 100% Abdi and Mahad both want to fix up their yard. They went to the same store and both bought rose bushes and evergreen plants Abdi spent $118 for 8 rose bushes and 2 evergreens. Mahad spent $82 for 5 rose bushes and 2 evergreens. 9) Multiple Choice: Which system of equation represents the situation above if "ris number of rose bushes and "e" is the number of evergreen plants purchased? (A) 8r+ 2e = 118 5r+ 2e = 82 (B) 8r + 2e = 82 5r +2e=118 (C) 8r+ 5e = 118 5r + 8e = 82 (D) 5r + 8e = 82 8r + 5e = 118 9. 10) How much does one evergreen plant cost? 10 11) How much does one rose bush cost? 12) If Ms. Mller plans to brighten up Banaadir Academy's landscape and she purchases 16 rose bushes and 24 evergreens, at the same place Abdi and Mahad got their plants, how much will she have to pay?

Answer 1

The transportation company is using vans and buses for the trip.

Part 5:

Let v represent the number of people on a van.

Let b represent the number of people on a bus.

A bus can hold 7 more than twice a van.

Mathematically,

`b=2v+7\quad eq.1`

Also, a total of 37 people can fit on one van and one bus combined.

Mathematically,

`v+b=37\quad eq.2`

Therefore, the system of equations for the given scenario is

`\begin{gathered} b=2v+7\quad eq.1 \\ v+b=37\quad eq.2 \end{gathered}`

Option C is the correct answer.

Part 6:

Let us solve the above system of equations to find out how many people can one van hold.

Substitute eq.1 into eq.2 and solve for v.

`\begin{gathered} v+b=37\quad eq.2 \\ v+(2v+7)=37 \\ v+2v+7=37 \\ 3v+7=37 \\ 3v=37-7 \\ 3v=30 \\ v=(30)/(3) \\ v=10 \end{gathered}`

Therefore, a van can hold 10 people.

Part 7:

How many people can one bus hold?

Substitute the value of v into eq.1

`\begin{gathered} b=2v+7\quad eq.1 \\ b=2(10)+7 \\ b=20+7 \\ b=27 \end{gathered}`

Therefore, a bus can hold 27 people.

Part 8:

If the school reserved 2 vans and 3 buses to go on the field trip, how many people are going to the field trip?

We know that each van can hold 10 people and each bus can hold 27 people.

`2v+3b=2\mleft(10\mright)+3\mleft(27\mright)=20+81=101`

Therefore, 101 people are going on the field trip.